Find the slope and y-intercept of the line that is perpendicular to y=-1/3+5 and passes through the points (-3,-7)

Remark

Perpendicular slopes are found by using the formula m1*m2 = - 1. That is followed by using the given point to determine the y intercept.

Solution

Step One

Find the slope of the new line

m1 = - 1/3

m2 = ??

m1 * m2 = - 1

(-1/3) * m2 = - 1

You could continue by changing (-1/3) to a decimal.

(-0.3333333333) * m2 = -1    Now divide by the decimal

m2 = - 1/ (-0.3333333333)

m2 = 3 which is what my calculator tells me the answer is.

Step Two

So far what you have is

y = 3x + b

Use the point (-3, -7) to get the y intercept.

-7 = 3(-3) + b

b - 9 = - 7

b = -7 + 9

b = 2

y = 3x + 2 Answer

Graph

The graph shown below is both lines plotted in desmos. The red line is y = 3x + 2 which is perpendicular to the given graph y = (-1/3)x +5 which is in blue.

The green dot is the point (-3 , - 7)