MPM1D Exam Review Chapter 6 – Linear Relations

1.  Match each linear equation with the graph that best suits it.

2.  Identify the slope and y-intercept for each of the relations
shown below. Then, write the equation of each line.

3.  Convert the following to slope-intercept form. Identify the slope and y-intercept.

a) b) c)

4.  Convert the following into standard form.

a) b) c)

5.  Determine the x-intercepts, y-intercepts, and slope of each of the following.

a) b) c)

6.  Graph the following lines on the same grid.

a) b) c) d) e)

7.  Determine whether the points A(2, -6), B(-3, 10) and C(-1, 1) are on the line .

8.  Find the equation of the line (in slope-intercept form) with a slope of that passes through the point (5, 7).

9.  Find the equation of the line, in point-slope form, of the line that has a slope of and passes through the point (-9, 12).

10.  Determine the equation of the line that is perpendicular to the line and has the same y-intercept as. Express your equation in slope-intercept form.

11.  Find the equation of the line that is parallel to the line and passes through (8, -7). Express your equation in point-slope form.

12.  Find the equation of the line perpendicular to that has the same x-intercept as . Express your answer in slope-intercept form.

13.  Find the equation of the line the passes through:

a) (3, -3) and (-3, 5) b) (5, 2) and (5, -3) c) (8, -5) and (2, 7)

14.  Holly downloads music from a site called MyTunes, which chargers a monthly membership fee plus an amount for each song downloaded. A 3-month record of her site activity is shown below.

Month / # of songs / Monthly Bill
January / 54 / $26.90
February / 38 / $25.30
March / 21 / $23.60

a)  Use two points from the table to determine an equation relating Holly’s monthly bill the number of songs she downloaded.

b)  Verify that the third point in the table satisfies your equation.

15.  Solve the following linear systems graphically. Check your solution.

a) and b) and

16.  Majida needs to park her car downtown while she takes a course. She can buy a monthly pass for $82, or she can register for $10 and then pay $6 each day to park. Under which conditions should Majida buy the monthly pass? When should she go with the second plan?

Chapter 6 Exam Review – Solutions

1) (a) -> (iii), (b) -> (vi), (c) -> (iv), (d) -> (ii), (e) -> (i), (f) -> (v) 2i) slope: 2, y-int: 3, ii) slope: , y-int: -2, iii) slope: 0, y-int: 8, iv) slope: undefined, y-int: none, 3a) , slope: , y-int: b) , slope: , y-int: c) , slope: , y-int: 4a) b) c) 5a) x-int: , y-int: -14, slope: b) x-int: -12, y-int: 15, slope: c) x-int: , y-int: , slope: 6)

7) A: yes, B: no, C: no 8) 9)

10) 11) 12)

13a) b) c)

14a) 15a) (2, -1) b) (2, 2)

16) If she is going to park more than 12 times, she
should buy the monthly pass. If she parks fewer
than 12 times, she should go with the second plan.
If she parks exactly 12 times, then it doesn’t
matter which plan she chooses.