Grade 9 · Lesson 20
Straight-line graphs
First master lines through the origin — y = mx. Then shift them with the intercept — y = mx + c.
Lines through the origin
Every equation y = mx is a straight line that passes through (0, 0). The number m is the gradient — how steep the line is.
Live graph
y = x
1
This line is uphill (positive). Gradient = rise ÷ run = 2 ÷ 2 = 1.
Key idea
- Always through the origin — when x = 0, y = 0.
- Steeper |m| means a steeper line.
- Negative m means the line slopes down left → right.
Table of values
Pick x-values, compute y from the equation, then plot the points. Straight line → points line up.
| x | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| y | -2 | -1 | 0 | 1 | 2 | 3 |
x = 2
(2, 2) lies on the line
Check yourself · y = mx
Type your answer, then check. Spelling and spaces are flexible.
Question 1 of 3
A line through the origin has gradient 3. Write its equation.
Remember
- y = mx → through (0, 0); m is steepness.
- y = mx + c → same steepness; c is where it hits the y-axis.
- Gradient = rise ÷ run. Plot intercept, then step along.