y-intercept – Where a Line Crosses the y-axis
The y-intercept of a line is the point where it crosses the y-axis, where x = 0. In the equation y = mx + c, this is the easiest feature of all to spot: the y-intercept is simply c, sitting there in plain sight, no calculation required.
That's exactly why the y-intercept is often the very first thing graphed when sketching a line by hand – plot the point (0, c), then use the gradient to find a second point, and the whole line is drawn.
Finding a y-intercept
At the y-intercept, x = 0. In y = mx + c, the y-intercept is simply c. For other forms, substitute x = 0 and solve for y.
Find the y-intercept of y = 5x − 9.
In y = mx + c form, the y-intercept is c: here c = −9. The y-intercept is the point (0, −9).
Real-Life Application
- Cost graphs: the y-intercept of a cost line often represents a fixed starting fee.
- Savings graphs: the y-intercept can show a starting balance before any deposits.
- Science experiments: the y-intercept can show a starting measurement at time zero.
Key Takeaways
- The y-intercept is where a line crosses the y-axis, where x = 0.
- In y = mx + c, the y-intercept is simply c.
- A point lies on the y-axis only when its x-coordinate is exactly 0.
Practice: y-intercept
Find the y-Intercept
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