Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Ask your questions and receive precise answers from experienced professionals across different disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Determine the intercepts of the line.

[tex]\( y = 6x + 13 \)[/tex]

[tex]\( x \)[/tex]-intercept: [tex]\(\quad \)[/tex]

[tex]\( y \)[/tex]-intercept: [tex]\((\quad , \quad)\)[/tex]


Sagot :

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].