Question

lesson 11: equation of lines
score: 69/100 answered: 11/15
question 11
give the equation of a line that goes through the point (-21,2) and is perpendicular to the line -7x - 9y = -18. give your answer in slope intercept form
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Explanation:

Step1: Find slope of given line

Rewrite $-7x - 9y = -18$ to slope-intercept form $y=mx+b$:

$$\begin{align*} -9y&=7x-18\\ y&=-\frac{7}{9}x+2 \end{align*}$$

Slope of given line is $m_1=-\frac{7}{9}$.

Step2: Find perpendicular slope

Perpendicular slope $m_2$ is negative reciprocal:

$$ m_2=\frac{9}{7} $$

Step3: Use point-slope form

Use point $(-21,2)$ and $m_2=\frac{9}{7}$ in $y-y_1=m(x-x_1)$:

$$ y-2=\frac{9}{7}(x+21) $$

Step4: Simplify to slope-intercept form

Expand and isolate $y$:

$$\begin{align*} y-2&=\frac{9}{7}x+27\\ y&=\frac{9}{7}x+29 \end{align*}$$

Answer:

$y=\frac{9}{7}x+29$