Find the Slope of the Perpendicular Line to the Line Through the Two Points (-12,3) , (11,-6)

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"><mn>3</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>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>12</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>12</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>23</mn></mrow><mrow><mn>9</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>23</mn></mrow><mrow><mn>9</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>23</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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Name | three hundred ninety-six million two hundred fifty-six thousand three hundred forty-eight |
---|

- 396256348 has 32 divisors, whose sum is
**923348160** - The reverse of 396256348 is
**843652693** - Previous prime number is
**2351**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 46
- Digital Root 1

Name | one billion five hundred eight million six hundred forty-five thousand eight hundred sixty-nine |
---|

- 1508645869 has 4 divisors, whose sum is
**1509632800** - The reverse of 1508645869 is
**9685468051** - Previous prime number is
**1531**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 52
- Digital Root 7

Name | one billion seven hundred twenty-one million one hundred seventy thousand four hundred thirty-one |
---|

- 1721170431 has 16 divisors, whose sum is
**2660747520** - The reverse of 1721170431 is
**1340711271** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 27
- Digital Root 9