Use <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> to calculate the equation of the line, where <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> represents the slope and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> represents the y-intercept.

To calculate the equation of the line, use the <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> format.

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>6</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Simplify the denominator.

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"><mn>5</mn></mstyle></math> .

Move the negative in front of the fraction.

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>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mn>3</mn><mo>+</mo><mi>b</mi><mo>=</mo><mn>6</mn></mstyle></math> .

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mn>3</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Move the negative in front of the fraction.

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"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to both sides of the equation.

To write <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</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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