Question

line v has an equation of $y = \frac{10}{9}x + 1$. line w includes the point $(-3, 3)$ and is perpendicular to line v. what is the equation of line w?
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 w

Perpendicular slopes are negative reciprocals. For line v with slope $\frac{10}{9}$, slope of w is $-\frac{9}{10}$.

Step2: Substitute point into slope-intercept

Use point $(-3, 3)$ and $m=-\frac{9}{10}$ in $y=mx+b$:
$3 = -\frac{9}{10}(-3) + b$

Step3: Calculate b value

$3 = \frac{27}{10} + b$
$b = 3 - \frac{27}{10} = \frac{30}{10} - \frac{27}{10} = \frac{3}{10}$

Step4: Write line w's equation

Combine slope and y-intercept in $y=mx+b$.

Answer:

$y = -\frac{9}{10}x + \frac{3}{10}$