X and Y Intercepts- How to Figure Out Intercepts from y=7x
What Are X and Y Intercepts?
Intercepts are the points where a line crosses the axes on a graph. The x-intercept is where the line hits the x-axis. The y-intercept is where it hits the y-axis.
That's it. Nothing fancy.
How to Find the Y-Intercept
Set x = 0 and solve for y.
For y = 7x:
y = 7(0) = 0
The y-intercept is the point (0, 0).
How to Find the X-Intercept
Set y = 0 and solve for x.
For y = 7x:
0 = 7x
x = 0 ÷ 7
x = 0
The x-intercept is also (0, 0).
Why Both Are the Same Here
This line passes through the origin. Every linear equation in the form y = mx (where there's no number added or subtracted) will have both intercepts at (0, 0).
The line y = 7x goes through the origin and gets steeper as x increases. That's because the slope is 7 — for every 1 unit you move right, you move up 7.
Intercepts at a Glance
| Intercept Type | Method | Result for y = 7x |
|---|---|---|
| Y-intercept | Set x = 0, solve for y | (0, 0) |
| X-intercept | Set y = 0, solve for x | (0, 0) |
Comparing Different Equations
| Equation | X-intercept | Y-intercept |
|---|---|---|
| y = 7x | (0, 0) | (0, 0) |
| y = 7x + 3 | (-3/7, 0) | (0, 3) |
| y = 7x - 2 | (2/7, 0) | (0, -2) |
| y = 3 | None | (0, 3) |
Notice how adding or subtracting a number changes everything. The +3 or -2 shifts the line up or down, creating separate intercepts.
How to Find Intercepts: Step-by-Step
Finding the Y-intercept
- Replace x with 0
- Solve the equation
- Write as an ordered pair (0, your answer)
Finding the X-intercept
- Replace y with 0
- Solve for x
- Write as an ordered pair (your answer, 0)
Common Mistakes
Forgetting to write the coordinate pair. Finding x = 0 isn't enough. You need (0, 0) for the y-intercept and (0, 0) for the x-intercept in this case.
Confusing the intercept with the slope. The slope is 7. The intercept is 0. These are different things.
Thinking the line doesn't cross the origin. Every line y = mx crosses (0, 0) because when x = 0, y = m(0) = 0.
The Bottom Line
For y = 7x, both intercepts are at the origin. That's the answer. If you understand set x=0, find y and set y=0, find x, you can handle any linear equation.