Question

Write the slope-intercept equation for the line that passes through (-3,-15)and is perpendicular to -6x+8y=3

Answer 1

First, let's solve the equation for y to determine the slope of the line.

-6x + 8y = 3

8y = 6x + 3

y = (6/8)x + 3/8 = (3/4)x + 3/8

Slope = 3/4

The slope of a line perpendicular to this one must be its negative reciprocal, or -4/3.

Now, use the point-slope form to find the other line:

y - y1 = m(x - x1)
y - (-15) = -4/3 [x - (-3)]
y + 15 = -4/3 (x + 3)
y + 15 = (-4/3)x - 4
y = (-4/3)x - 4 - 15
y = (-4/3)x - 19

And there you have it! By showing you the steps, I hope this will help with other problems of this type.