Question

the equation for line c can be written as $y = \frac{3}{4}x - 2$. line d, which is perpendicular to line c, includes the point (6, -3). what is the equation of line d?
write the equation in slope-intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Find slope of line d

Perpendicular slopes are negative reciprocals.
Slope of line c is $\frac{3}{4}$, so slope of line d is $-\frac{4}{3}$.

Step2: Use point to find y-intercept

Substitute $x=6$, $y=-3$, $m=-\frac{4}{3}$ into $y=mx+b$.
$$-3 = -\frac{4}{3}(6) + b$$
$$-3 = -8 + b$$
$$b = -3 + 8 = 5$$

Step3: Write slope-intercept equation

Combine slope and y-intercept.

Answer:

$y = -\frac{4}{3}x + 5$