Finding the <em>x</em>- and <em>y</em>- Intercepts From An Equation of a Line
Finding the x- and y- Intercepts from an Equation of a Line
Recognizing that the x- intercept occurs when y is zero and that the y- intercept occurs when x is zero, gives us a method to find the intercepts of a line from its equation. To find the x- intercept, let \(y=0\) and solve for x. To find the y- intercept, let \(x=0\) and solve for y.
Find the x- and y- Intercepts from the Equation of a Line
Use the equation of the line. To find:
- the x- intercept of the line, let \(y=0\) and solve for \(x\).
- the y- intercept of the line, let \(x=0\) and solve for \(y\).
Example
Find the intercepts of \(2x+y=6\).
Solution
We will let \(y=0\) to find the x- intercept, and let \(x=0\) to find the y- intercept. We will fill in the table, which reminds us of what we need to find.
To find the x- intercept, let \(y=0\).
| Let y = 0. | |
| Simplify. | |
| The x-intercept is | (3, 0) |
| To find the y-intercept, let x = 0. | |
| Let x = 0. | |
| Simplify. | |
| The y-intercept is | (0, 6) |
The intercepts are the points \(\left(3,0\right)\) and \(\left(0,6\right)\) as shown in the table below.
| \(2x+y=6\) | |
| \(x\) | \(y\) |
| 3 | 0 |
| 0 | 6 |
Example
Find the intercepts of \(4x–3y=12\).
Solution
| To find the x-intercept, let y = 0. | |
| Let y = 0. | |
| Simplify. | |
| The x-intercept is | (3, 0) |
| To find the y-intercept, let x = 0. | |
| Let x = 0. | |
| Simplify. | |
| The y-intercept is | (0, −4) |
The intercepts are the points (3, 0) and (0, −4) as shown in the table below.
| \(4x-3y=12\) | |
| \(x\) | \(y\) |
| 3 | 0 |
| 0 | \(-4\) |
This lesson is part of:
Graphs and Equations