Rewrite the equation as <math><mstyle displaystyle="true"><mfrac><mrow><mi>y</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

Multiply both sides of the equation by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor.

Rewrite the expression.

Simplify the right side.

Combine <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mi>x</mi></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math> .

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.

Reorder terms.

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>5</mn></mrow></mfrac></mstyle></math>

y-intercept: <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

Slope: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>

y-intercept: <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

Reorder terms.

Create a table of the <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> values.

Graph the line using the slope and the y-intercept, or the points.

Slope: <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>5</mn></mrow></mfrac></mstyle></math>

y-intercept: <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math>

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