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>5</mn><mi>x</mi></mstyle></math> from both sides of the equation.

Divide each term in <math><mstyle displaystyle="true"><mn>6</mn><mi>y</mi><mo>=</mo><mn>7</mn><mo>-</mo><mn>5</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>6</mn><mi>y</mi><mo>=</mo><mn>7</mn><mo>-</mo><mn>5</mn><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>6</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 the right side.

Move the negative in front of the fraction.

Write in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> form.

Reorder <math><mstyle displaystyle="true"><mfrac><mrow><mn>7</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>5</mn><mi>x</mi></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Reorder terms.

Remove parentheses.

Using the slope-intercept form, the slope is <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> and a given point <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></mrow></mstyle></math> to substitute for <math><mstyle displaystyle="true"><msub><mi>x</mi><mrow><mn>1</mn></mrow></msub></mstyle></math> and <math><mstyle displaystyle="true"><msub><mi>y</mi><mrow><mn>1</mn></mrow></msub></mstyle></math> in the point-slope form <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><msub><mi>y</mi><mrow><mn>1</mn></mrow></msub><mo>=</mo><mi>m</mi><mrow><mo>(</mo><mi>x</mi><mo>-</mo><msub><mi>x</mi><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow></mstyle></math> , which is derived from the slope equation <math><mstyle displaystyle="true"><mi>m</mi><mo>=</mo><mfrac><mrow><msub><mi>y</mi><mrow><mn>2</mn></mrow></msub><mo>-</mo><msub><mi>y</mi><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mi>x</mi><mrow><mn>2</mn></mrow></msub><mo>-</mo><msub><mi>x</mi><mrow><mn>1</mn></mrow></msub></mrow></mfrac></mstyle></math> .

Simplify the equation and keep it in point-slope form.

Simplify <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>)</mo></mrow></mstyle></math> .

Rewrite.

Simplify by adding zeros.

Apply the distributive property.

Combine <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>⋅</mo><mo>-</mo><mn>5</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Combine <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> from both sides of the equation.

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

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

Combine the numerators over the common denominator.

Simplify the numerator.

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

Subtract <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>25</mn></mstyle></math> .

Write in <math><mstyle displaystyle="true"><mi>y</mi><mo>=</mo><mi>m</mi><mi>x</mi><mo>+</mo><mi>b</mi></mstyle></math> form.

Reorder terms.

Remove parentheses.

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