Question

write the equation of a line that is perpendicular to $y = -\frac{2}{7}x + 9$ and that passes through the point $(4, -6)$.

Explanation:

Step1: Find the slope of the perpendicular line

The slope of the given line is $-\frac{2}{7}$. The slope of a line perpendicular to it is the negative - reciprocal. So the slope $m$ of the perpendicular line is $\frac{7}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(4,-6)$ and $m = \frac{7}{2}$. Substitute these values: $y-(-6)=\frac{7}{2}(x - 4)$.

Step3: Simplify the equation

First, simplify $y + 6=\frac{7}{2}(x - 4)$. Distribute $\frac{7}{2}$: $y+6=\frac{7}{2}x-14$. Then subtract 6 from both sides to get the slope - intercept form: $y=\frac{7}{2}x-20$.

Answer:

$y=\frac{7}{2}x - 20$