Question

Determine and state an equation of the line perpendicular to the line 8x + 6y = 15 and passing through the point (3,-4)

Answer 1

4y - 3x = -25

Explanation:

The equation of a line in point-slope form is expressed as

y - y0 = m(x - x0)

(x0, y0) is the point

m is the slope

Given

(x0, y0) = (3, -4)

Also given the equation;

8x + 6y = 15

Rewrite in standard form;

6y = -8x+15

y = -8/6 x + 15/6

y = -4/3 x + 5/2

Slope m = -4/3

Since the required line is perpendicular to the given line =,

Slope = -1/(-4/3) = 3/4

Substitute into the formula;

y - (-4) = 3/4(x-3)

y + 4 = 3/4(x-3)

4(y+4) = 3(x-3)

4y + 16 = 3x - 9

4y - 3x = -9-16

4y - 3x = -25

This gives the required equation