Question

Find an equation of the line passing through the point (-4,6) that is perpendicular to the line y=7/2x+5. Work please.

Answer 1

Answer:

y = $-\frac{2}{7}$x + 4$\frac{6}{7}$

Step-by-step explanation:

We are to find the equation of line 1 which passes through point (-4,6)

Line 1 is perpendicular to line 2.

The equation of line 2 is; y = $\frac{7}{2}$x + 5

The slope of line 2 is  $\frac{7}{2}$

Because the product of two perpendicular line is -1;

The slope of line 1 is -1 ÷  $\frac{7}{2}$ =  $\frac{-2}{7}$

Taking another point (x,y) on line 1;

Slope = change in y ÷ change in x

$\frac{-2}{7}$ = $\frac{y - 6}{x - -4}$

y - 6 =  $\frac{-2}{7}$(x + 4)

y - 6 =  $\frac{-2}{7}$x - $\frac{8}{7}$

y =  $\frac{-2}{7}$ - $\frac{8}{7}$ + 6

y = $-\frac{2}{7}$x + 4$\frac{6}{7}$