Graph to equation
m comes from rise/run between two points; b is where the line crosses the y-axis.
Why it works
m = 3, b = 2 → y = 3x + 2.
Graphs · y = mx + b · 5.4
Write the equation.
To write a line’s equation from its graph, read the slope (rise/run) for m and the y-intercept for b, then write y = mx + b. A line through (0, 2) and (1, 5) has m = 3, b = 2 → y = 3x + 2.
See it work.
Watch the method
Write the equation
Read m and b, then y = mx + b.
1
Find the slope
Slope = rise ÷ run between the two points.
2
Find the y-intercept
Use a point to solve for b, then write y = mx + b.
Practice until it feels automatic.
Your turn
Work it out.
Type y = mx + b.
streak 0
best 0
Your answer:
The idea underneath.
From easy to tricky.
Write the equation (y = mx + b) of the line shown.
1
Find the slope
Slope = rise ÷ run between the two points. m = 3
2
Find the y-intercept
Use a point to solve for b, then write y = mx + b. y = 3x - 4
Write the equation (y = mx + b) of the line shown.
1
Find the slope
Slope = rise ÷ run between the two points. m = -2
2
Find the y-intercept
Use a point to solve for b, then write y = mx + b. y = -2x + 1
Write the equation (y = mx + b) of the line shown.
1
Find the slope
Slope = rise ÷ run between the two points. m = 3
2
Find the y-intercept
Use a point to solve for b, then write y = mx + b. y = 3x + 4
Where students slip.
Trap
Putting the slope as b (or vice versa).
Fix
m multiplies x; b is the intercept.
Trap
Reading the intercept off the wrong axis.
Fix
The y-intercept is on the y-axis (x = 0).
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
C2
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
C3
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
C4
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
Apply
Apply (4)
A1
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
A2
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
A3
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
A4
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
Extension
Extension (4)
E1
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
E2
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
E3
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.
E4
Write the equation (y = mx + b) of the line shown.
Need a hint?
- Find the slope for m.
- Find the y-intercept for b; write y = mx + b.