Find the Slope of the Perpendicular Line to the Line Through the Two Points (-11.3,-11.6) , (12.8,4.5)

Slope is equal to the change in <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> over the change in <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> , or rise over run.

The change in <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> is equal to the difference in x-coordinates (also called run), and the change in <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> is equal to the difference in y-coordinates (also called rise).

Substitute in the values of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> into the equation to find the slope.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>11.6</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4.5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>11.6</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>11.3</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>12.8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>11.3</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>16.1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>24.1</mn></mstyle></math> .

The slope of a perpendicular line is the negative reciprocal of the slope of the line that passes through the two given points.

The slope of the perpendicular line is <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>0.66804979</mn></mrow></mfrac></mstyle></math> .

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