What is the slope of the line that passes through (3,2) and is perpendicular to the line that passes through (-2,3) and (2,-3)?

Question

I just want someone to check my answer and if I get it wrong to show me how to do it! My answer is 2/3

Answer 1

The slope of the line that passes through the points

(-2, 3) and (2, -3) is found by the following formula:

(y1 - y2) / (x1 - x2). This can also be referred to as the rise over the run.

In the above equation

Y1 = 3

Y2 = -3

X1 = -2

X2 = 2

So the formula for calculating the slope is:

(3 - -3) / (-2 -2) = 6/-4 = -3/2.

The line perpendicular would have a negative reciprocal slope compared to -3/2 or a slope of 2/3.

Answer 2

Step 1:  Find the equation of the line that passes through (-2,3) and (2, -3).

 

The slope of this line will be

 

m = (-3 - 3)/(2 - (-2))

m = -6/4

 

The equation is y = -(6/4)x + b

 

We must find the y-intercept of equation by substituting values from any of these points.  Lets pick (-2,3).

 

3 = -(6/4)(-2) + b

3 = 3 +b

0 = b

 

Our equation of the line that passes through both of these points is      y = -(6/4)x

 

 

Step 2: Find the slope of the line that is perpendicular to the line from previous answer and passes through (3,2).

 

Perpendicular slopes have negative reciprocals.  This means the slope of the line that passes through (3,2) is

 

4/6 = 2/3