The slope-intercept form is <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> , where <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> is the slope and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> is the y-intercept.

Subtract <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi></mstyle></math> from both sides of the equation.

Divide each term by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>12</mn><mo>-</mo><mn>3</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify <math><mstyle displaystyle="true"><mfrac><mrow><mn>12</mn></mrow><mrow><mo>-</mo><mn>4</mn></mrow></mfrac><mo>+</mo><mfrac><mrow><mo>-</mo><mn>3</mn><mi>x</mi></mrow><mrow><mo>-</mo><mn>4</mn></mrow></mfrac></mstyle></math> .

Simplify each term.

Divide <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> .

Dividing two negative values results in a positive value.

Reorder <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn><mi>x</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math> .

Rewrite in slope-intercept form.

Find the values of <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> using the form <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> .

The slope of the line is the value of <math><mstyle displaystyle="true"><mi>m</mi></mstyle></math> , and the y-intercept is the value of <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> .

Slope: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

y-intercept: <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math>

Slope: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mstyle></math>

y-intercept: <math><mstyle displaystyle="true"><mo>-</mo><mn>3</mn></mstyle></math>

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