Find the equation of the line through (8,-6) which is perpendicular to the line y=x3-7.

Give your answer in the form y=mx+b

y = (-1/3) (x + 10)

Step-by-step explanation:

The slope of the new (perpendicular) line is the negative reciprocal of the slope of the given line, which appears to be 3. Thus, the perpendicular line has the slope - 1/3.

Using the slope-intercept form y = mx + b, and substituting the givens, we obtain:

y = mx + b = > - 6 = (-1/3) (8) + b, or

-6 = - 8/3 + b. We must solve for the y-intercept, b:

Multiplying all three terms by 3 removes the fraction:

-18 = - 8 + 3b. Thus, - 10 = 3b, and so b must be - 10/3.

The desired equation is

y = (-1/3) x - 10/3, or

y = (-1/3) (x + 10)