Title: Unit 4 Quiz
Course: Technical Math for Industry

Q: Compute the slope of the line between the points (-1,3) and (4, 22).
A: (a choice with no text)
If right: The slope of the line that contains then points (-1,3) and (4,22) is equal to .
If wrong: Be sure that the difference of y-coordinates is in the numerator and the difference of the x-coordinates is in the denominator. Also, be sure to use the coordinates in the same "order" in the numerator and denominator. That is, if the numerator is y-coordinate of first point minus y-coordinate of second point, then the denominator should be the x-coordinate of the first point minus the x-coordinate of the second point.
If wrong: Be sure that the difference of y-coordinates is in the numerator and the difference of the x-coordinates is in the denominator. Also, be sure to use the coordinates in the same "order" in the numerator and denominator. That is, if the numerator is y-coordinate of first point minus y-coordinate of second point, then the denominator should be the x-coordinate of the first point minus the x-coordinate of the second point.
If wrong: Be sure that the difference of y-coordinates is in the numerator and the difference of the x-coordinates is in the denominator. Also, be sure to use the coordinates in the same "order" in the numerator and denominator. That is, if the numerator is y-coordinate of first point minus y-coordinate of second point, then the denominator should be the x-coordinate of the first point minus the x-coordinate of the second point.

Q: Compute the slope of the line graphed below.
A: (a choice with no text)
If wrong: To compute the slope of the line, find the slope between 2 points on the line. Remember, the slope of the line is the "rise" divided by the "run" (that is the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line).
If right: The points (0,3) and (3,1) are on the line, so its slope is .
If wrong: To compute the slope of the line, find the slope between 2 points on the line. Remember, the slope of the line is the "rise" divided by the "run" (that is the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line).
If wrong: To compute the slope of the line, find the slope between 2 points on the line. Remember, the slope of the line is the "rise" divided by the "run" (that is the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line).

Q: x | y
1 | 2
3 | 11
5 | 20
9 | 38

Find the slope of the line represented by the table above.
- 9 (Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.)
- 4.5 (Correct. The slope between any two points represented by the table is 4.5. For example, the slope between (1,2) and (3,11) is .)
A: 4.5
If wrong: Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.
If wrong: Incorrect. Identify two sets of values in this table, and then find the difference between the y-values and the difference between the x-values. This will lead you to the slope of the line.

Q: The point (-2,1) is on a line with slope 3. Which of the following points are also on the line?
- (0,3) (Incorrect. The slope between (-2,1) and (0,3) is 1.)
- (0,5) (Incorrect. The slope between (-2,1) and (0,5) is 2.)
- (0,7) (Correct. The slope between (-2,1) and (0,7) is 3.)
- (0,1) (Incorrect. The slope between (-2,1) and (0,1) is 0.)
A: (0,7)

Q: Three points are said to be collinear if they all lie on the same line. One way to show that three points are collinear is to show that the slope between any two pairs of the points is the same.

If P=(1, 5), Q=(2, 2), and R=(4, -1), are P, Q, and R collinear?
- No (Correct. The three points are not collinear. The slope between P and Q is, the slope between P and R is , and the slope between Q and R is .)
- Yes (Incorrect. What is the slope between (1, 5) and (2, 2)? What is the slope between (2, 2) and (4, -1)? Did you find the same values or different values?)
A: No

Q: What is the y-intercept of the line with equation
A: (a choice with no text)
If wrong: Incorrect. The y-intercept of the line is the point on the line corresponding to Substitute into the equation to find the value of the y-coordinate.
If right: Correct. The y-intercept of the line is the point on the line corresponding to According to the line's equation, if then so the y-intercept is
If wrong: Incorrect. The y-intercept of the line is the point on the line corresponding to Substitute into the equation to find the value of the y-coordinate.
If wrong: Incorrect. The y-intercept of the line is the point on the line corresponding to Substitute into the equation to find the value of the y-coordinate.

Q: Find the x-intercept of the line represented by the table.

x | y
0 | -35
1 | -30
2 | -25
3 | -20
- (7,0) (Correct. The x-intercept of the line is the point (x,0) that lies on the line. Using the pattern described in the table, the slope of the line is 5, so the points (4,-15), (5,-10), (6,-5), and (7,0) are also on the line, showing that the x-intercept is (7,0).)
- (0, 35) (Incorrect. The x-intercept of the line is the point (x,0) on the line. Use the pattern in the table to find the value of the x-coordinate when y = 0.)
- (6,0) (Incorrect. The x-intercept of the line is the point (x,0) on the line. Use the pattern in the table to find the value of the x-coordinate when y = 0.)
- (-35,0) (Incorrect. The x-intercept of the line is the point (x,0) on the line. Use the pattern in the table to find the value of the x-coordinate when y = 0.)
A: (7,0)

Q: What is the y-intercept of the line with equation
- (0, 7) (Correct. The y-intercept of the line is the point (0, y) that lies on the line. If x = 0, then 5y - 7(0) = 35, so 5y=35, and therefore y = 7, showing that the y-intercept is (0, 7).)
- (-5, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Substitute x = 0 into the equation to find the value of the y-coordinate.)
- (0, -7) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Substitute x = 0 into the equation to find the value of the y-coordinate.)
- (0, -5) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Substitute x = 0 into the equation to find the value of the y-coordinate.)
A: (0, 7)

Q: Find the y-intercept of the line represented by the table.

x | y
2 | -25
3 | -20
4 | -15
5 | -10
- (5, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
- (0, -35) (Correct. The y-intercept of the line is the point (0, y) that lies on the line. Using the pattern described in the table, the slope of the line is 5, so the points (1, -30) and (0, -35) are also on the line, showing that the y-intercept is (0, -35).)
- (-35, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
- (6, 0) (Incorrect. The y-intercept of the line is the point (0, y) that lies on the line. Use the pattern in the table to find the value of the y-coordinate when x = 0.)
A: (0, -35)

Q: What is the y-intercept of the line with equation ?
- (0, 7) (Incorrect. The y-intercept of the line with equation is the point (0, b). What is the value of b in this equation?)
- (0, 4) (Correct. The y-intercept of the line with equation is the point (0, b), so the correct answer is (0, 4).)
- (0, -4) (Incorrect. The y-intercept of the line with equation is the point (0, b). What is the value of b in this equation?)
- (0, -7) (Incorrect. The y-intercept of the line with equation is the point (0, b). What is the value of b in this equation?)
A: (0, 4)

Q: Identify the slope and y-intercept of the line with equation .
- slope = -5, y-intercept = (0, -3) (Incorrect. Remember, the line with equation has slope m and y-intercept (0, b).)
- slope = -3, y-intercept = (-5, 0) (Incorrect. Remember, the line with equation has slope m and y-intercept (0, b).)
- slope = 3, y-intercept = (0, -5) (Incorrect. Remember, the line with equation has slope m and y-intercept (0, b).)
- slope = -3, y-intercept = (0, -5) (Correct. The line with equation has slope m and y-intercept (0, b), so the slope of this line is -3 and its y-intercept is (0, -5).)
A: slope = -3, y-intercept = (0, -5)

Q: Which of the following is the equation of the line shown below?
A: (a choice with no text)
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?
If right: Correct. The y-intercept is (0, -2) and the points (0, -2) and (-2, 1) are on the line, so the slope is . Therefore the slope intercept form of the equation is .
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?
If wrong: Incorrect. Find the y-intercept and slope of the line. Which equation represents this information?

Q: Which graph shows the line ?
A: (a choice with no text)
If wrong: Incorrect. Use the equation to determine the slope and y-intercept of the line. Which graph shows the correct y-intercept? Use the slope to find other points on the line (for example, when , what will the y-coordinate be?)
If right: Correct. The line has slope 5 and y-intercept (0, 3). Graphs A and B both have slope 5, but graph A has a y-intercept of (0, -3), while graph B has the correct y-intercept of (0, 3).
If wrong: Incorrect. Use the equation to determine the slope and y-intercept of the line. Which graph shows the correct y-intercept? Use the slope to find other points on the line (for example, when , what will the y-coordinate be?)
If wrong: Incorrect. Use the equation to determine the slope and y-intercept of the line. Which graph shows the correct y-intercept? Use the slope to find other points on the line (for example, when , what will the y-coordinate be?)

Q: Which of the following is the equation of the line graphed below?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the line? (Note that it contains the points (0, 2) and (1, -1).) What is its y-intercept?
If wrong: Incorrect. What is the slope of the line? (Note that it contains the points (0, 2) and (1, -1).) What is its y-intercept?
If wrong: Incorrect. What is the slope of the line? (Note that it contains the points (0, 2) and (1, -1).) What is its y-intercept?
If right: Correct. The line shown has slope -3 (since it contains the points (0, 2) and (1, -1)) and its y-intercept is (0, 2), so the equation of the line is .

Q: Which of the following equations represent the line that has slope -3 and goes through the point (2, 5)?
A: (a choice with no text)
If wrong: Incorrect. This equation would be the point slope form of the line with slope -3 going through the point Since the line has the correct slope, we should still check to see if this is an alternate way to represent the given line. To do this we need to check whether is on the line Replacing x with 2 and y with 5, but , so when and
If wrong: Incorrect. The slope of the line represented by the equation is 3 and the slope of the line we are given is -3, so this equation cannot represent the given line.
If wrong: Incorrect. This equation would be the point slope form of the line with slope -3 going through the point Since the line has the correct slope, we should still check to see if this is an alternate way to represent the given line. To do this we need to check whether is on the line Replacing x with 2 and y with 5, but , so when and
If right: Correct. The point slope form of the line with slope m going through the point is so the point slope form of the given line is

Q: Which of the following points lie on the line
- Only (3, -2) lies on the line. (Incorrect. Check whether either (or both) of the points lie on the line by determining whether the coordinates of each point satisfies the given equation.)
- Only (2, 3) lies on the line. (Incorrect. Check whether either (or both) of the points lie on the line by determining whether the coordinates of each point satisfies the given equation.)
- Both points lie on the line. (Correct. Both points lie on the line. The equation is the point slope form of the line with slope -5 going through the point (3, -2). However, when = (2, 3), and , so the point (2, 3) also lies on the line.)
- Neither point lies on the line. (Incorrect. Check whether either (or both) of the points lie on the line by determining whether the coordinates of each point satisfies the given equation.)
A: Both points lie on the line.

Q: What is the slope of the line with equation ?
- 3 (Incorrect. To determine the slope of the line, solve for . The equation is then in the slope intercept form of the line: . The value of is the slope.)
- 2 (Incorrect. To determine the slope of the line, solve for . The equation is then in the slope intercept form of the line: . The value of is the slope.)
- -2 (Correct. To determine the slope of the line, solve for : if , then , so . This is the slope intercept form of the line, so the slope is -2.)
A: -2
If wrong: Incorrect. To determine the slope of the line, solve for . The equation is then in the slope intercept form of the line: . The value of is the slope.

Q: Convert the point slope equation into standard form.
A: (a choice with no text)
If wrong: To express the equation in standard form, multiply both sides of the equation by 4 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.
If wrong: To express the equation in standard form, multiply both sides of the equation by 4 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.
If right: Correct. If then , so so and therefore
If wrong: To express the equation in standard form, multiply both sides of the equation by 4 to eliminate the fraction. Then distribute the -3 through and bring the x and y terms to one side of the equation and the constants to the other side.

Q: At the end of every month Michael deposits $70 into his savings account. After 11 months, Michael's account had a total of $1250. Which of these equations expresses the amount Michael has in his savings account after months?
A: (a choice with no text)
If wrong: Incorrect. The equation will represent the line with slope 70 going through the point (11, 1250). What is the point slope form of the line?
If wrong: Incorrect. The equation will represent the line with slope 70 going through the point (11, 1250). What is the point slope form of the line?
If right: Correct. The equation will represent the line with slope 70 going through the point (11, 1250). The point slope form of this line is .
If wrong: Incorrect. The equation will represent the line with slope 70 going through the point (11, 1250). What is the point slope form of the line?

Q: Which of the following lines is parallel to the line ?
A: (a choice with no text)
If wrong: Incorrect. Two lines are parallel if they have the same slope. Remember, in the slope intercept form of the line, , the slope is the value of . What is the slope of the line ?
If wrong: Incorrect. Two lines are parallel if they have the same slope. Remember, in the slope intercept form of the line, , the slope is the value of . What is the slope of the line ?
If right: Correct. Two lines are parallel if they have the same slope. The slope of the line is -7, so the slope of a parallel line also has to be -7.
If wrong: Incorrect. Two lines are parallel if they have the same slope. Remember, in the slope intercept form of the line, , the slope is the value of . What is the slope of the line ?

Q: Which of following lines are parallel to the line ?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the lin e ? What should the slope of a parallel line be?
If wrong: Incorrect. What is the slope of the lin e ? What should the slope of a parallel line be?
If right: Correct. The given line has a slope of 7 and any line parallel to it will also have that slope.
If wrong: Incorrect. What is the slope of the lin e ? What should the slope of a parallel line be?

Q: Which equation represents the line that goes through (4, -1) and is parallel to the line ?
A: (a choice with no text)
If right: Correct. The slope intercept form of the line is , so the slope of our line is . The equation is the point slope form of the line with slope that goes through the point (4, -1), so this is the equation we want.
If wrong: Incorrect. Determine the slope of the line by expressing the line in slope intercept form (solving for first). Then, use the fact that (4, -1) is on the line to find the point slope form of the line.
If wrong: Incorrect. Determine the slope of the line by expressing the line in slope intercept form (solving for first). Then, use the fact that (4, -1) is on the line to find the point slope form of the line.
If wrong: Incorrect. Determine the slope of the line by expressing the line in slope intercept form (solving for first). Then, use the fact that (4, -1) is on the line to find the point slope form of the line.

Q: Which of the following lines are parallel to the line that goes through the points (2, -1) and (8, -4)?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the line containing (2, -1) and (8, -4)? What should the slope of a parallel line be?
If wrong: Incorrect. What is the slope of the line containing (2, -1) and (8, -4)? What should the slope of a parallel line be?
If right: Correct. The slope of the line between (2, -1) and (8, -4) is so the slope of a line parallel to it will be also.
If wrong: Incorrect. What is the slope of the line containing (2, -1) and (8, -4)? What should the slope of a parallel line be?

Q: Which of these lines is NOT parallel to the line ?
A: (a choice with no text)
If wrong: Incorrect. Express each line in slope intercept form to determine its slope. What slope will parallel lines have?
If right: Correct. If , then and this line has slope -7. Since the line has slope 7, the two lines are not parallel.
If wrong: Incorrect. Express each line in slope intercept form to determine its slope. What slope will parallel lines have?
If wrong: Incorrect. Express each line in slope intercept form to determine its slope. What slope will parallel lines have?

Q: What is the slope of a line that is perpendicular to the line ?
- 8 (Incorrect. The given line has slope 8. The slope of a perpendicular line will be the opposite reciprocal of this number. What is the opposite reciprocal of 8?)
- -8 (Incorrect. The given line has slope 8. The slope of a perpendicular line will be the opposite reciprocal of this number. What is the opposite reciprocal of 8?)
A: (a choice with no text)
If wrong: Incorrect. The given line has slope 8. The slope of a perpendicular line will be the opposite reciprocal of this number. What is the opposite reciprocal of 8?
If right: Correct. Since the given line has slope 8, a line perpendicular to it will have slope (the opposite reciprocal of 8).

Q: What is the slope of a line that is perpendicular to the line ?
- 5 (Incorrect. What is the slope of the given line? What should the slope of a perpendicular line be?)
- -5 (Correct. Since the line has slope , any line perpendicular to it will have slope -5 (the opposite reciprocal of ).)
A: -5
If wrong: Incorrect. What is the slope of the given line? What should the slope of a perpendicular line be?
If wrong: Incorrect. What is the slope of the given line? What should the slope of a perpendicular line be?

Q: Which line is perpendicular to the line graphed below?
A: (a choice with no text)
If right: Correct. Since the graphed line has slope (it goes through the points (0, -2) and (2, -1)), any line perpendicular to it will have slope -2 (the opposite reciprocal of ).
If wrong: Incorrect. Identify two points that this line goes through, and find the slope of the line. Then use the opposite reciprocal of that number to identify a perpendicular line.
If wrong: Incorrect. Identify two points that this line goes through, and find the slope of the line. Then use the opposite reciprocal of that number to identify a perpendicular line.
If wrong: Incorrect. Identify two points that this line goes through, and find the slope of the line. Then use the opposite reciprocal of that number to identify a perpendicular line.

Q: Which of these equations represents the line that goes through (-1, 5) and is perpendicular to the line ?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the line ? What should the slope of a perpendicular line be? Use the point slope form to determine the equation of the line through (-1, 5).
If wrong: Incorrect. What is the slope of the line ? What should the slope of a perpendicular line be? Use the point slope form to determine the equation of the line through (-1, 5).
If right: Correct. The slope of is , so any line perpendicular to it will have slope -3 (the opposite reciprocal of ). The equation is the point slope form of the line with slope -3 that goes through (-1, 5).
If wrong: Incorrect. What is the slope of the line ? What should the slope of a perpendicular line be? Use the point slope form to determine the equation of the line through (-1, 5).

Q: Which line is perpendicular to the line graphed below?
A: (a choice with no text)
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?
If right: Correct. The graphed line has slope since it goes through the points (0, 1) and (-4, 2). Any line perpendicular to the graphed line must have slope 4 (the opposite reciprocal of ).
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?
If wrong: Incorrect. What is the slope of the graphed line? What should the slope of a perpendicular line be?