To determine the intercepts of the line given by the equation [tex]\( y = 8x - 18 \)[/tex], let's find the [tex]\( y \)[/tex]-intercept and the [tex]\( x \)[/tex]-intercept separately.
### Finding the [tex]\( y \)[/tex]-Intercept
The [tex]\( y \)[/tex]-intercept occurs where the line crosses the [tex]\( y \)[/tex]-axis. This happens when [tex]\( x = 0 \)[/tex].
1. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = 8(0) - 18
\][/tex]
2. Simplify the equation:
[tex]\[
y = -18
\][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept is [tex]\( (0, -18) \)[/tex].
### Finding the [tex]\( x \)[/tex]-Intercept
The [tex]\( x \)[/tex]-intercept occurs where the line crosses the [tex]\( x \)[/tex]-axis. This happens when [tex]\( y = 0 \)[/tex].
1. Substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[
0 = 8x - 18
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
8x - 18 = 0
\][/tex]
[tex]\[
8x = 18
\][/tex]
[tex]\[
x = \frac{18}{8}
\][/tex]
[tex]\[
x = \frac{9}{4}
\][/tex]
[tex]\[
x = 2.25
\][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept is [tex]\( \left(2.25, 0\right) \)[/tex].
### Summary
The intercepts of the line [tex]\( y = 8x - 18 \)[/tex] are:
- [tex]\( y \)[/tex]-intercept: [tex]\( (0, -18) \)[/tex]
- [tex]\( x \)[/tex]-intercept: [tex]\( \left(2.25, 0\right) \)[/tex]
