Title: M5.2 Graphing Quiz
Course: Technical Math for Industry > Section: Module 5.2 Graphing

Q: Which ordered pair represents the plotted point on the graph?
- (5, 2) (Incorrect. You may not have noticed that when you stopped under the point on the x-axis, the label on the x-axis was , not 5.)
- (2, 5) (Incorrect. You mixed up the order of the x-coordinates and the y-coordinates, and you did not notice that the label on the x-axis under the point is , not 5.)
- (, 2) (Correct. Begin at the origin (0, 0). Move left along the x-axis until you are under the point. The label on the x-axis here is . This is the x-coordinate, the first number in the ordered pair. From , move up to the point. The number with which the point is aligned on the y-axis is 2. This is the y-coordinate, the second number in the ordered pair.)
- (2, ) (Incorrect. You mixed up the order of the x-coordinates and the y-coordinates.)
A: (, 2)

Q: Which of the following ordered pairs is represented by a point located on the y-axis?
- (0, 3) (Correct. Whenever the x-coordinate in an ordered pair is 0, the point it represents is located on the y-axis.)
- (, 0) (Incorrect. You may have mixed up the x-coordinates and y-coordinates. When the y-coordinate is 0, the point is located on the x-axis, not the y-axis.)
- (4, ) (Incorrect. For a point located on the y-axis, the x-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.)
A: (0, 3)
Feedback: Incorrect. For a point located on the y-axis, the x-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)
Feedback: Correct. When , , so and . When , , so and . When , , so and .
Feedback: Incorrect. You may have correctly substituted the x-values and tried to solve for y, but mistakenly subtracted when you should have added. Check your work by substituting both values in at once.
Feedback: 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.
Feedback: 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 (2, 0) and the y-intercept is (0, ). (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 (10, 0) and the y-intercept is (0, ). (Correct. Substitute to find the y-intercept: , so . Substitute to find the x-intercept: , so . The x-intercept is at (10, 0) and the y-intercept is at (0, ).)
- The x-intercept is (0, 10) and the y-intercept is (, 0). (Incorrect. You switched the x-values and the y-values.)
- The x-intercept is (0, ) and the y-intercept is (10, 0). (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 .)
A: The x-intercept is (10, 0) and the y-intercept is (0, ).

Q: Which of the following ordered pairs is a solution to the equation ?
- (2, ) (Incorrect. You probably switched the values of x and y. If you substitute these values correctly you get: Simplify: or This is not a true statement, so the ordered pair (2) is not a solution to the equation.)
- (3, ) (Incorrect. You probably made a mistake with signs. Substitute and into the equation: Simplify: or . This is not a true statement, so the ordered pair (3, ) is not a solution to the equation.)
- (0, 4) (Incorrect. You probably switched the values of x and y. If you substitute these values correctly you get: Simplify: or This is not a true statement, so the ordered pair (0, 4) is not a solution to the equation.)
- (, 2) (Correct. Substitute and into the equation: Simplify: or The statement is true, so (, 2) is a solution to the equation.)
A: (, 2)

Q: Orlando bought a new couch for $2,904, using the furniture store's finance plan. He will pay $121 a month for 24 months. Which equation can Orlando use to find out how much money he still owes after each month of the plan?
A: (a choice with no text)
Feedback: Incorrect. The amount of money, y, that Orlando still owes equals the cost minus what he has paid. This equation would represent the cost plus what he has paid after x months.
Feedback: Incorrect. The amount of money, y, that Orlando still owes equals the cost minus what he has paid, but you have reversed these two amounts.
Feedback: Incorrect. The amount of money, y, that Orlando still owes equals the cost minus what he has paid. However, this equation shows only how much he has paid.
Feedback: Correct. If he pays off $121 per month, then he will pay dollars in x months. The amount of money, y, that Orlando still owes equals the cost minus what he has paid. So .

Q: What is the slope of the line described by the equation ?
- 1 (Incorrect. The slope for a line written in the form is m. You may have mistakenly used the coefficient of y instead of x.)
- 3 (Incorrect. The slope for a line written in the form is m. You may have made a mistake with a sign when you rewrote the equation. If you write the equation in this form, the coefficient of x will be negative.)
A: (a choice with no text)
Feedback: Correct. Rewrite the equation as . The slope for a line written in the form is m. Therefore the slope, m, is .
Feedback: Incorrect. You may have thought that, since the slope is , you needed to divide some numbers from the equation. The slope for a line written in the form is m.

Q: What is the slope of the line that contains the points and ?
A: (a choice with no text)
Feedback: Correct. , , , and Substitute the values into the slope formula and simplify.
Feedback: Incorrect. You evaluated , but the slope formula is
Feedback: 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
Feedback: Incorrect. You evaluated , but the slope formula is

Q: Which line has an undefined slope?
A: (a choice with no text)
Feedback: Incorrect. You may have thought that since the equation is set to 0, the slope is undefined. However, this equation can be rewritten as , which tells you that the line it describes has a slope of 3.
Feedback: Incorrect. You may have thought that this is a vertical line. However, any line of the form constant is horizontal, and has a slope of 0.
Feedback: Correct. This line contains the points (18, 0) and (18, 1). Its slope would be: This is undefined.
Feedback: Incorrect. You may have thought that since x has no coefficient, there is no slope. 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 ?
A: (a choice with no text)
Feedback: 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.
Feedback: 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 ignored the negative sign of the slope. The slope of the line is , not 1.
Feedback: Correct. The point is the y-intercept of the line, so . The slope, m, is . Substituting these values into the equation , you find .
Feedback: 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.

Q: Write the equation of the line with a slope of 4 that contains the point (5, 8).
A: (a choice with no text)
Feedback: Incorrect. You may have correctly substituted (5, 8) into , but then incorrectly added 20 instead of subtracting 20 from both sides when solving for b.
Feedback: Incorrect. You correctly substituted the slope 4 into the equation . However, when you substituted (5, 8) into the equation to find b, you mixed up the x-value and the y-value.
Feedback: Incorrect. Though you correctly substituted the slope 4 into , you then substituted the y-value, 8, from the ordered pair for b. Instead, you should substitute the coordinates of the point (5, 8) for x and y in and solve for b.
Feedback: Correct. Substitute the slope 4 into : Substitute the coordinates of the point (5, 8) for x and y: Solve for b: , so Rewrite with and :

Q: Write the equation of the line that passes through and in slope-intercept form.
A: (a choice with no text)
Feedback: 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.
Feedback: Correct. Find the slope using the given points: Substitute either point for x and y into : Solve for b: , so or Substitute the values of m and b into .
Feedback: 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.
Feedback: 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 added instead of subtracting from both sides of the equation.

Q: Which of the following lines is parallel to the line ?
A: (a choice with no text)
Feedback: Correct. The given line is written in the form . Since , the slope is . The slope of any parallel line would be the same number. Therefore, its slope would be . So it must have an equation in the form . The given equation has this form.
Feedback: Incorrect. You may have thought that a line parallel to , which has a slope of , could have an opposite slope. But parallel lines have the same slope, with different y-intercepts.
Feedback: Incorrect. You chose a line that has the same slope as , but it does not have a different y-intercept, so the lines are not parallel. They are the same line.
Feedback: Incorrect. You chose a line that is perpendicular to , not parallel to it. Parallel lines have the same slope.

Q: Which of the following is the equation of the line that is perpendicular to and goes through the point ?
A: (a choice with no text)
Feedback: Incorrect. A perpendicular line will have a slope that is the negative reciprocal of the given slope. You mistakenly used the opposite of the slope of . Then you used this to find b and write your equation.
Feedback: Incorrect. A perpendicular line will have a slope that is the negative reciprocal of the given slope. You mistakenly used the reciprocal of the slope of . Then you used this to find b and write your equation.
Feedback: Incorrect. You found the line that is parallel to and goes through instead of the line that is perpendicular to the given line through that point.
Feedback: Correct. The slope of is . The slope of a perpendicular line is 8, the negative reciprocal of . Its equation has the form . To find b, substitute for x and y: or , so The equation of the line is .

Q: Which ordered pair is a solution to the inequality ?
A: (a choice with no text)
Feedback: Correct. Substitute for x and y in the inequality: Simplify: or The statement is true, so is a solution to the inequality.
Feedback: Incorrect. You may have thought that this was a solution because, after substituting for x and y and simplifying, you get 16 on both sides of the inequality. However, is a false statement, so is not a solution.
Feedback: Incorrect. You may have thought this was a solution because, after substituting for x and y and simplifying, you get 16 on both sides of the inequality. However, is a false statement, so is not a solution.
Feedback: Incorrect. Substituting these values into the inequality gives you , or . Since is a false statement, is not a solution.

Q: Which of the following inequalities is graphed below?
A: (a choice with no text)
Feedback: Incorrect. You may not have noticed that the boundary line is solid, not dashed. You also may not have checked to see if an ordered pair from the shaded region made this inequality true.
Feedback: Incorrect. You may not have noticed that the boundary line is solid. The points along the line are included in the solution, so the inequality symbol should be .
Feedback: Correct. The boundary line shown has a slope of and a y-intercept of 1. Since it is solid, the inequality must be or . The ordered pair (0, 2) falls in the shaded region, and is a solution to the first inequality: or
Feedback: Incorrect. You may not have checked to see if an ordered pair from the shaded region made this inequality true. If you substitute (0, 2) into this inequality, you get , or . This statement is false, so this is not the inequality that is graphed.