To determine the intercepts of the line given by the equation [tex]\( y = 6x + 13 \)[/tex], we need to find both the [tex]\( x \)[/tex]-intercept and the [tex]\( y \)[/tex]-intercept.
### Finding the Y-Intercept:
The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis. This occurs where [tex]\( x \)[/tex] is zero.
1. Substitute [tex]\( x = 0 \)[/tex] into the equation.
[tex]\[
y = 6(0) + 13
\][/tex]
2. Simplify the equation.
[tex]\[
y = 13
\][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept is the point:
[tex]\[
(0, 13)
\][/tex]
### Finding the X-Intercept:
The [tex]\( x \)[/tex]-intercept is the point where the line crosses the [tex]\( x \)[/tex]-axis. This occurs where [tex]\( y \)[/tex] is zero.
1. Set [tex]\( y = 0 \)[/tex] in the equation:
[tex]\[
0 = 6x + 13
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[
0 = 6x + 13 \implies 6x = -13 \implies x = \frac{-13}{6}
\][/tex]
Therefore, the [tex]\( x \)[/tex]-intercept is the point:
[tex]\[
\left(-\frac{13}{6}, 0\right)
\][/tex]
### Summary
- The [tex]\( x \)[/tex]-intercept is [tex]\(\left(-\frac{13}{6}, 0\right)\)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\((0, 13)\)[/tex].
