### Home > AC > Chapter 8 > Lesson 8.2.2 > Problem8-57

8-57.

For the line $y=2x+6$:

1. What is the $x$-intercept?

2. What is the slope of any line perpendicular to the given line?

The $x$-intercept is where $y=0$.

Subtract $6$ from both sides.

Divide by $2$ on both sides.

$y=2x+6$
$0=2x+6$

$−6=2x$

$−3=x$

The $x$-intercept is $(−3,0)$.

The slope of a line perpendicular to another line is the negative reciprocal of the other line's slope.

Example:
Line (a): $y=4x+7$
$m=4$

$\text{The line perpendicular to line (a) has the slope }-\frac{1}{4}.$