Co-ordinate Geometry
288. The Y-Intercept · Where the line crosses the vertical axis
The line always intersects the y-axis at B, and the distance OB equals the y-intercept c.
The y-intercept is the y-coordinate of the point where a line crosses the y-axis (where x = 0). In y = mx + c this value is c, the distance OB measured along the y-axis.
What this lesson covers
Try to break it
Drag B up and down along the y-axis. The line slides with B, and the y-intercept readout c equals the signed distance from O to B. Push B above the origin and c is positive; below, c is negative; at O, c = 0 (the line passes through the origin).
How you build it
Mark the y-intercept and draw a line through it.
- On the y-axis, count 4 units up from the origin O and click to mark point B. This height is the y-intercept c.
- Draw a straight line passing through B: click B, then any other point. However you slope the line, it still crosses the y-axis at B, so its y-intercept c = 4.
The proof, step by step
Prove that the line meets the y-axis at a distance equal to the y-intercept c.
- The equation of a straight line is y = mx + c.
- The constant term 'c' represents the y-coordinate where the line meets the y-axis.
- Therefore, the y-intercept is simply the value of c.
Worked example
The equation of a straight line is given as 2y - 6x + 8 = 0. What is the y-intercept of this line?
Rearrange to slope-intercept form: 2y = 6x - 8 → y = 3x - 4. The constant term is -4, so the y-intercept is -4.
- 4
- -4 — correct
- 3
- -3