write the slope intercept equation for the line that passes through

Question

(-14,-3) and is perpendicular to -7x-4y=-4

Answer 1

Perpendicular means that it needs to have opposite reciprocal slopes

so -7x-4y = -4 needs to be solve for y to get the slope.

-4y = -4 +7x then y=1-7/4 x

so the slope that u need is -7/4, the opposite reciprocal is 4/7 (use this as m into point-slope)

y+3 = 4/7(x+14)

y+3=4/7x + 8

y=4/7x + 5

Answer 2

Start with the line equation and put it into slope intercept format:

-7x -4y = -4 (solve for y)

-7x + 4 = 4y

y = -7/4x + 1

The slope of the line is -7/4.  To get a perpendicular line you need the negative reciprical.  Flip the slope and change the sign.

Perpendicular line slope is 4/7.

Use the point now (-14, -3) and slope = 4/7.

y - -3 = 4/7(x - -14)

y + 3 = 4/7x + 14*4/7

y + 3 = 4/7x + 8

y = 4/7x + 8 - 3

y = 4/7x + 5