Find the Equation with a Point and Slope What is the equation of the line that passes through the point (6,-8) and has a slope of -2/3 ?

What is the equation of the line that passes through the point <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>)</mo></mrow></mstyle></math> and has a slope of <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> ?

Use the formula for the equation of a line to find <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Substitute the value of <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> into the equation.

Substitute the value of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> into the equation.

Substitute the value of <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> into the equation.

Find the value of <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Rewrite the equation as <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⋅</mo><mn>6</mn><mo>+</mo><mi>b</mi><mo>=</mo><mo>-</mo><mn>8</mn></mstyle></math> .

Simplify each term.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Move the leading negative in <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> into the numerator.

Factor <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Move all terms not containing <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>8</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Now that the values of <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> (slope) and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> (y-intercept) are known, substitute them into <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> to find the equation of the line.

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