what is the equation of the line that is perpendicular to the given line and passes through the point (3…

Answer:

D. $5x - 3y=15$

Explanation:

Step1: Find slope of given line

Use two - point formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-3,2)$ and $(x_2,y_2)=(2, - 1)$. Then $m_1=\frac{-1 - 2}{2+3}=\frac{-3}{5}$.

Step2: Find slope of perpendicular line

If two lines are perpendicular, $m_1\times m_2=-1$. Given $m_1 =-\frac{3}{5}$, then $-\frac{3}{5}\times m_2=-1$, so $m_2=\frac{5}{3}$.

Step3: Use point - slope form

The point - slope form is $y - y_0=m(x - x_0)$. Here $(x_0,y_0)=(3,0)$ and $m=\frac{5}{3}$. So $y-0=\frac{5}{3}(x - 3)$.

Step4: Convert to standard form

$y=\frac{5}{3}(x - 3)$ expands to $y=\frac{5}{3}x-5$. Multiply through by 3 to get $3y = 5x-15$, which can be rewritten as $5x-3y = 15$.