Linear Functions & y = mx + b — Drills
Linear Functions & y = mx + b has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Readmb
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Give the slope and y-intercept of y = -6x + 3.
Worked answer
m = -6, b = 3
m = -6
b = 3
Problem 2
Give the slope and y-intercept of y = -1x + 5.
Worked answer
m = -1, b = 5
m = -1
b = 5
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For y = 2x + 1, find y when x = 7.
Worked answer
15
2(7) = 14
14 + 1 = 15
Problem 2
For y = 4x - 2, find y when x = 0.
Worked answer
-2
4(0) = 0
0 - 2 = -2
Intercepts
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the x-intercept of y = 3x + 3.
Worked answer
-1
0 = 3x + 3
3x = -3
x = -1
Problem 2
Find the x-intercept of y = -4x + 20.
Worked answer
5
0 = -4x + 20
-4x = -20
x = 5
Rearrange
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write 3x + 4y = 4 in slope-intercept form.
Worked answer
y = -3/4x + 1
4y = -3x + 4
Divide every term by 4.
y = -34x + 1
Problem 2
Write 5x + 3y = -15 in slope-intercept form.
Worked answer
y = -5/3x + -5
3y = -5x + -15
Divide every term by 3.
y = -53x + -5
From two points
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Write the equation of the line through (0, -7) and (5, 8).
Worked answer
y = 3x + -7
b = -7
m = 8 - (-7)5 = 3
y = 3x - 7
Problem 2
Write the equation of the line through (0, -2) and (2, -6).
Worked answer
y = -2x + -2
b = -2
m = -6 - (-2)2 = -2
y = -2x - 2
From a graph
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A line has m = 2 and b = 3. Which point lies on it?
- (5, 15)
- (5, 12)
- (5, 14)
- (5, 13)
Worked answer
(5, 13)
y = 2(5) + 3 = 13
So (5, 13) is on the line.
Problem 2
A line has m = 4 and b = 3. Which point lies on it?
- (3, 15)
- (3, 16)
- (3, 14)
- (3, 17)
Worked answer
(3, 15)
y = 4(3) + 3 = 15
So (3, 15) is on the line.
Word problems
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A tank holds 510 litres and drains at 30 litres per minute. After how many minutes is it empty?
Worked answer
17
0 = -30x + 510
30x = 510
x = 17 minutes
Problem 2
A club charges $18 to join plus $25 a month. Write the cost equation.
Worked answer
y = 25x + 18
b = 18
m = 25
y = 25x + 18