Question

Find the slope and y-intercet of the line that is perpendicular to y= 3 x − 3 and passes through the point ( − 8,-2)

Answer 1

Answer:

Step-by-step explanation:

If a line has a slope of $3$, then the line perpendicular to it has a slope of $-\frac{1}{3}$ (opposite reciprocal).

With this, we can construct a line in slope-intercept form:

$y = mx + b$

Where $m$ is the slope of the line and $b$ is the y-intercept.

We already know the slope of the line, so we can plug it into the equation:

$y = -\frac{1}{3}x + b$

We also know that the line passes through the point $(-8, -2)$, so we can plug this into the equation to get $b$:

$-2 = -\frac{1}{3}(-8) + b$

$-2 = \frac{8}{3} + b$

$b = -\frac{14}{3}$