Question

line s has an equation of $y = \frac{1}{3}x - 5$. line t is perpendicular to line s and passes through $(-2, 9)$. what is the equation of line t?
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 t

Perpendicular slopes are negative reciprocals. The slope of line $s$ is $\frac{1}{3}$, so the slope of line $t$ is $-3$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-3$, $x_1=-2$, $y_1=9$:
$y - 9 = -3(x - (-2))$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y - 9 = -3(x + 2)$
$y - 9 = -3x - 6$
$y = -3x - 6 + 9$
$y = -3x + 3$

Answer:

$y = -3x + 3$