Title: Unit 13 Quiz
Course: Technical Math for Industry

Q: Which point represents the ordered pair ?
- Point C (Incorrect. This point represents the ordered pair . You began at the origin and moved three units in the negative direction (left) along the x-axis, but then you moved two units down (in the negative direction). You should have moved two units up (in the positive direction).)
- Point A (Incorrect. This point represents the ordered pair . You began at the origin and moved three units in the positive direction (right) along the x-axis before moving up two units, but you should have first moved three units to the left (in the negative direction).)
- Point B (Correct. Begin at the origin and move three units in a negative direction (left) along the x-axis. Then move two units up (in a positive direction). Point B is located there.)
- Point D (Incorrect. This point represents the ordered pair . You should first move three units to the left along the x-axis, and then two units up.)
A: Point B

Q: Which of the following ordered pairs is represented by a point located on the x-axis?
A: (a choice with no text)
If right: Correct. Whenever the y-coordinate in an ordered pair is 0, the point it represents is located on the x-axis.
If wrong: Incorrect. You may have mixed up the x-coordinates and y-coordinates. When the x-coordinate is 0, the point is located on the y-axis, not the x-axis.
If wrong: Incorrect. For a point located on the x-axis, the y-coordinate is 0. The x-coordinate in this ordered pair is positive, and the y-coordinate is negative, so the point would be located in Quadrant IV.
If wrong: Incorrect. For a point located on the x-axis, the y-coordinate is 0. Both coordinates in this ordered pair are positive, so the point would be located in Quadrant I.

Q: Which table of values could be generated by the equation ?
A: (a choice with no text)
If right: Correct. When , , so and . When , , so and . When , , so and .
If wrong: Incorrect. You may have switched the values of x and y and made a mistake with the signs. Check your work by substituting both values in at once.
If wrong: Incorrect. You may have correctly substituted the x-values and tried to solve for y, but mistakenly added when you should have subtracted. Check your work by substituting both values in at once.
If wrong: Incorrect. You switched the values of x and y. That is, when , . When , . When , .

Q: Identify the x-intercept and y-intercept of the line .
- The x-intercept is and the y-intercept is . (Incorrect. You switched the x-values and the y-values.)
- The x-intercept is and the y-intercept is . (Incorrect. You chose the coefficients of the variables x and y as your x-intercept and y-intercept. Instead, you need to substitute into to find the y-intercept, and substitute to find the x-intercept.)
- The x-intercept is and the y-intercept is . (Incorrect. You mixed up the two intercepts. The x-intercept is the point where the line crosses the x-axis. This happens when . The y-intercept is the point where the line crosses the y-axis. This happens when .)
- The x-intercept is and the y-intercept is . (Correct. Substitute to find the y-intercept: , so . Substitute to find the x-intercept: , so . The x-intercept is at and the y-intercept is at .)
A: The x-intercept is and the y-intercept is .

Q: For which of the following equations is not a solution?
A: (a choice with no text)
If wrong: Incorrect. You may have made a mistake in subtraction. Remember that subtracting is the same as adding the opposite and the sum will have the same sign as the addend with the greater absolute value. or or The statement is true, so the ordered pair is a solution to the equation.
If right: Correct. Substitute the values for x and y from the ordered pair into the equation: Simplify: or Since the statement is not true, the ordered pair is not a solution to the equation.
If wrong: Incorrect. You may have mixed up the values of x and y when substituting them into the equation. or or The statement is true, so the ordered pair is a solution to the equation.
If wrong: Incorrect. You may have made a mistake with a sign. Remember that a negative times a positive is negative. or or The statement is true, so the ordered pair is a solution to the equation.

Q: Jonathan bought a new computer for $2,016, using the electronics store's finance plan. He will pay $112 a month for 18 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
A: (a choice with no text)
If wrong: Incorrect. The amount of money, y, that Jonathan still owes equals the cost minus what he has paid. This equation would represent the cost plus what he has paid after x months.
If wrong: Incorrect. The amount of money, y, that Jonathan still owes equals the cost minus what he has paid, but you have reversed these two amounts.
If wrong: Incorrect. The amount of money, y, that Jonathan still owes equals the cost minus what he has paid. However, this equation shows only how much he has paid.
If right: Correct. If he pays off $112 per month, then he will pay dollars in x months. The amount of money, y, that Jonathon still owes equals the cost minus what he has paid. So .

Q: Find the slope of the line graphed below.
- 3 (Correct. Starting at the point , move three units up and then one unit to the right to get to the point . The rise is 3 and the run is 1.)
A: 3
If wrong: Incorrect. First, you probably wrote the slope as instead of . Second, if you move from to , you are going up and to the right, so both the rise and the run are positive. This means that the slope is positive.
If wrong: Incorrect. If you move from to , you are going up and to the right, so both the rise and the run are positive. This means that the slope is positive.
If wrong: Incorrect. You wrote the slope as instead of .

Q: What is the slope of the line that contains the points and ?
- 4 (Incorrect. You evaluated , but the slope formula is)
- 3 (Incorrect. You evaluated , but the slope formula is)
A: (a choice with no text)
If right: Correct. , , , and Substitute the values into the slope formula and simplify.
If wrong: Incorrect. When you use the slope formula, , be careful to subtract in the same order in the numerator and denominator. That is, the first numbers on top and bottom should be the coordinates from the same point. The slope of this line is given by

Q: Which line has a slope of 0?
A: (a choice with no text)
If right: Correct. This line contains the points and . Its slope would be: The slope is 0.
If wrong: Incorrect. You may have thought that this is a horizontal line. However, any line of the form constant is vertical, and has an undefined slope.
If wrong: Incorrect. You may have thought that since the equation is set to 0, the slope is 0. However, this equation can be rewritten as , which tells you that the line it describes has a slope of .
If wrong: Incorrect. You may have thought that since x has no coefficient, the slope is 0. However, this equation can be written as , which means the line it describes has a slope of 1.

Q: What is the equation of a line that goes through the point and has a slope of 1?
A: (a choice with no text)
If wrong: Incorrect. The slope-intercept form of a line is , where m is equal to the slope of the line and b is equal to the y-intercept. You mixed up the values of the slope and the y-intercept when substituting the values into the equation.
If wrong: Incorrect. The slope-intercept form of a line is , where m is equal to the slope of the line and b is equal to the y-intercept. You may not have noticed the negative sign of the slope in the equation. The slope of the line is 1, not .
If wrong: Incorrect. The slope-intercept form of a line is , where m is equal to the slope of the line and b is equal to the y-intercept. You correctly substituted the value of the slope into the equation. However, you used the y-intercept as the coefficient of y, instead of substituting for b.
If right: Correct. The point is the y-intercept of the line, so . The slope, m, is 1. Substituting these values into the equation , you find .

Q: Write the equation of the line with a slope of that contains the point .
A: (a choice with no text)
If right: Correct. Substitute the slope into : Substitute the coordinates of the point for x and y: Solve for b: , so Rewrite with and :
If wrong: Incorrect. You may have correctly substituted into , but then incorrectly subtracted 6 instead of adding 6 to both sides when solving for b.
If wrong: Incorrect. You correctly substituted the slope into the equation . However, when you substituted into the equation to find b, you mixed up the x-value and the y-value.
If wrong: Incorrect. Though you correctly substituted the slope into , you then substituted the y-value, , from the ordered pair for b. Instead, you should substitute the coordinates of the point for x and y in and solve for b.

Q: Write the equation of the line that passes through and in slope-intercept form.
A: (a choice with no text)
If right: Correct. Find the slope using the given points: Substitute either point for x and y into : Solve for b: , so Substitute the values of m and b into .
If wrong: Incorrect. When calculating the slope, you probably subtracted the denominator in the wrong order. You then used the incorrect slope to find the y-intercept of the line.
If wrong: Incorrect. Though you found the correct slope of the line, you made a mistake when finding b. After substituting the point for x and y in , you incorrectly subtracted 4 instead of adding 4 to both sides of the equation.
If wrong: Incorrect. When finding the slope, you mistakenly set the difference of the x-values over the difference of the y-values instead of the difference of the y-values over the difference of the x-values. You then used the incorrect slope to find the y-intercept.

Q: Which of the following lines is perpendicular to the line ?
A: (a choice with no text)
If wrong: Incorrect. You may have seen that is the negative reciprocal of , and thought that this made the two lines perpendicular. However, these are the y-intercepts of the lines. In order for the two lines to be perpendicular, the slopes must be negative reciprocals of each other.
If right: Correct. The given line is written in the form . Since , the slope is . The slope of any perpendicular line would be the negative reciprocal of this slope. Therefore, its slope would be . So it must have an equation in the form . The given equation has this form.
If wrong: Incorrect. You may have thought that a line perpendicular to , which has a slope of , has a slope that is the reciprocal of . However, the slopes of perpendicular lines are negative reciprocals of each other.
If wrong: Incorrect. You may have thought that a line perpendicular to , which has a slope of , has a slope that is the opposite of . However, the slopes of perpendicular lines are negative reciprocals of each other.

Q: Which of the following is the equation of the line that is parallel to and goes through point ?
A: (a choice with no text)
If wrong: Incorrect. You found the line that is perpendicular to and goes through instead of the line that is parallel to the given line through that point.
If right: Correct. The slope of is . A parallel line has the same slope. Its equation has the form . To find b, substitute for x and y: , or , so The equation of the line is .
If wrong: Incorrect. A parallel line has the same slope as the given line. However, you mistakenly used the reciprocal of the slope of . Then you used this to find b and write your equation.
If wrong: Incorrect. A parallel line has the same slope as the given line. You mistakenly used the opposite of the slope of . Then you used this to find b and write your equation.

Q: The ordered pair is a solution to which of the following inequalities?
A: (a choice with no text)
If wrong: Incorrect. Substitute for x and y: or This is a false statement, so is not a solution to this inequality.
If wrong: Incorrect. You may have thought that was a solution to this inequality because you ended up with 6 on each side of the inequality symbol. However, is a false statement, so is not a solution to the inequality.
If wrong: Incorrect. is not a solution because , or , is a false statement.
If right: Correct. Substitute for x and y in the inequality: or Since this statement is true, the ordered pair is a solution.

Q: Which of the following inequalities is graphed below?
A: (a choice with no text)
If right: Correct. The boundary line of the graphed inequality has a slope of and a y-intercept of . Because it is dashed, the inequality must be or . The ordered pair (2, 0) falls in the shaded region and is a solution to the second inequality: or
If wrong: Incorrect. You may not have noticed that the boundary line is dashed. The points along the line are not included in the solution, so the inequality symbol should be .
If wrong: Incorrect. You may not have checked to see if an ordered pair from the shaded region made this inequality true. If you substitute (2, 0) into this inequality, you get , or . This statement is false, so this is not the inequality that is graphed.
If wrong: Incorrect. You may not have noticed that the boundary line is dashed, not solid. You also may not have checked to see if an ordered pair from the shaded region makes this inequality true.