Find the Slope of the Perpendicular Line to the Line Through the Two Points (6,-9) , (0,4)

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>9</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Simplify the denominator.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Move the negative in front of the fraction.

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

Cancel the common factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> as <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> .

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mo>-</mo><mfrac><mrow><mn>6</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> .

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

Multiply <math><mstyle displaystyle="true"><mfrac><mrow><mn>6</mn></mrow><mrow><mn>13</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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