Give the slope-intercept form of the equation of the line that is perpendicular to
–7x – 8y = 12 and contains P(–3, 1).

y = 8x/7 + 31/7

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)

The equation of the given line is

–7x – 8y = 12

Rearranging t to take the slope intercept form, it becomes

8y = - 7x - 12

y = - 7x/8 - 12/8

Comparing with the slope intercept form, slope = - 7/8

If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line that contains P(–3, 1) is 8/7

To determine the intercept, we would substitute m = 8/7, x = - 3 and y = 1 into y = mx + c. It becomes

1 = 8/7 × - 3 + c

1 = - 24/7 + c

c = 1 + 24/7

c = 31/7

The equation becomes

y = 8x/7 + 31/7

the answer will be the last one