To find the intercepts of the line given by the equation [tex]\( 5x - 12y = 80 \)[/tex], we'll follow these steps:
### Finding the [tex]\(x\)[/tex]-intercept
1. Set [tex]\( y = 0 \)[/tex]: The [tex]\(x\)[/tex]-intercept occurs where the line crosses the x-axis, which means that [tex]\( y = 0 \)[/tex].
2. Substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
5x - 12(0) = 80
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
5x = 80
\][/tex]
[tex]\[
x = \frac{80}{5}
\][/tex]
[tex]\[
x = 16
\][/tex]
4. State the [tex]\( x\)[/tex]-intercept as an ordered pair:
[tex]\[
(x, y) = (16, 0)
\][/tex]
### Finding the [tex]\(y\)[/tex]-intercept
1. Set [tex]\( x = 0 \)[/tex]: The [tex]\(y\)[/tex]-intercept occurs where the line crosses the y-axis, which means that [tex]\( x = 0 \)[/tex].
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
5(0) - 12y = 80
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
-12y = 80
\][/tex]
[tex]\[
y = \frac{80}{-12}
\][/tex]
[tex]\[
y = -\frac{80}{-12} \quad \text{(simplifying negative signs)}
\][/tex]
[tex]\[
y \approx 6.67
\][/tex]
4. State the [tex]\( y\)[/tex]-intercept as an ordered pair:
[tex]\[
(x, y) = (0, 6.67)
\][/tex]
### Summary
- The [tex]\( x\)[/tex]-intercept is [tex]\((16, 0)\)[/tex].
- The [tex]\( y\)[/tex]-intercept is [tex]\((0, 6.67)\)[/tex].
