y-intercept — Grade 7 Math, what it means and where it is taught
The output when x = 0 — where the line crosses the vertical axis.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Slope-intercept form — y = mx + b, with m the slope and b the y-intercept.
Practise this idea
12 questions in the course bank use y-intercept, in Functions, Linear Functions & y = mx + b, Slope & the Forms of a Line, Graphing Quadratics, Polynomial Functions & Their Graphs. The first 8 are below; the rest are in those units.
Problem 1
What is the y-intercept of y = 5x - 3?
Worked answer
-3
At x = 0: y = -3
Problem 2
A line passes through (2, 9) and (5, 21). Find its y-intercept.
Worked answer
1
9 = 4(2) + b
9 = 8 + b, so b = 1
Check with (5,21): 20 + 1 = 21 ✓
Problem 3
A line has slope -2 and passes through (3, 1). Find its y-intercept.
Worked answer
7
1 = -2(3) + b
1 = -6 + b
b = 7
Problem 4
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 5
Give the slope and y-intercept of y = -23x + 7.
Worked answer
m = -2/3, b = 7
m = -23
b = 7
Problem 6
Find the y-intercept of y = 8x.
Worked answer
0
y = 8(0) = 0
The line passes through the origin
Problem 7
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 8
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