Linear Functions & y = mx + b — Practice
Two numbers describe a whole line: where it starts, and how fast it changes.
What these questions cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Slope — How much y changes for each 1 that x increases.
- y-intercept — The output when x = 0 — where the line crosses the vertical axis.
- Slope-intercept form — y = mx + b, with m the slope and b the y-intercept.
- x-intercept — The x value when y = 0 — where it crosses the x-axis.
- Height — The perpendicular distance from the base to the opposite corner.
Problem 1
Give the slope and y-intercept of y = 5x - 3.
Worked answer
m = 5, b = -3
m = 5
b = -3 — the sign belongs to it
Problem 2
Give the slope and y-intercept of y = -23x + 7.
Worked answer
m = -2/3, b = 7
m = -23
b = 7
Problem 3
For y = 4x - 9, find y when x = 3.
Worked answer
3
4(3) - 9
= 12 - 9 = 3
Problem 4
For y = -2x + 11, find x when y = 1.
Worked answer
5
-2x + 11 = 1
-2x = -10
x = 5
Problem 5
Find the y-intercept of y = 8x.
Worked answer
0
y = 8(0) = 0
The line passes through the origin
Problem 6
Write 3x + y = 10 in slope-intercept form.
Worked answer
y = -3x + 10
Subtract 3x
y = -3x + 10
Note the slope is negative
Problem 7
Write 4x + 2y = 14 in slope-intercept form.
Worked answer
y = -2x + 7
2y = -4x + 14
y = -2x + 7
Problem 8
Find the slope of 6x - 3y = 12.
Worked answer
2
-3y = -6x + 12
y = 2x - 4
m = 2
Problem 9
Write the equation of the line through (0, -4) and (3, 5).
Worked answer
y = 3x - 4
b = -4
m = 5 - (-4)3 - 0 = 3
y = 3x - 4
Problem 10
Find the x-intercept of y = 2x - 12.
Worked answer
6
0 = 2x - 12
2x = 12
x = 6
Problem 11
A line has m = -3 and b = 4. Which point is on it?
- (1, 1)
- (1, 7)
- (0, -3)
- (3, 4)
Worked answer
(1, 1)
y = -3(1) + 4 = 1
So (1, 1) works
Check another: -3(3) + 4 = -5 ≠ 4
Problem 12
A gym charges $50 to join plus $30 a month. Write the cost equation.
Worked answer
y = 30x + 50
b = 50
m = 30
y = 30x + 50
Problem 13
A tank holds 480 litres and drains at 16 litres per minute. After how many minutes is it empty?
Worked answer
30
0 = -16x + 480
16x = 480
x = 30 minutes
Problem 14
Find the slope and y-intercept of x2 + y5 = 1.
Worked answer
m = -5/2, b = 5
5x + 2y = 10
2y = -5x + 10
y = -52x + 5
Problem 15
A line passes through (2, 7) and (6, 19). Find its y-intercept.
Worked answer
1
m = 19 - 76 - 2 = 3
7 = 3(2) + b
b = 1
Problem 16
Two candles burn down. Candle A is y = -2x + 24 cm; candle B is y = -3x + 30 cm. After how many minutes are they the same height?
Worked answer
6
-2x + 24 = -3x + 30
x = 6
Both are 12 cm tall then ✓