MPM1D – Exam Review
Chapter 5: Slope
1. Direct variation
 Has the formula 𝑦 = 𝑚𝑥 (m is slope)
 The graph passes through (0,0)
 There is no fixed cost or starting value
2. Partial variation
 Has the formula 𝑦 = 𝑚𝑥 + 𝑏 (m is slope, b is y-intercept)
 Does not pass through (0,0)
 Has a fixed cost or starting value
3. Slope is the rate of change a.k.a. the steepness of a line.
 In an equation, slope is represented by m
 It can be calculated from a graph or a table of values by using:
rise
𝑦2 − 𝑦1
𝑚=
or
𝑚=
run
𝑥2 − 𝑥1
 In a word problem, the slope is always given as a comparison between two
units. Look for units written as fractions or the words per, each, every, etc.
E.g.: km/hr, dollars per shift, number of sales every day
 The slope of a horizontal line is 0.
 The slope of a vertical line is undefined.
4. Parallel lines have the same slope.
 Find the slope of a line parallel to 𝑦 = −3𝑥 + 4:
5. Perpendicular lines have negative reciprocal slopes.
 Find the slope of a line perpendicular to 𝑦 = −3𝑥 + 4:

2
Find the slope of a line perpendicular to 𝑦 = 3 𝑥 − 1: