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# Writing Linear Equations in Slope-Intercept Form

## Converting from Standard and Point-Slope Forms to Slope-Intercept Form

Conversion from standard and point-slope forms to slope-intercept form is achieved by adding and subtracting terms from each side of the equations, and then multiplying or dividing. This is best illustrated using examples.

Example 1

Write 6x + 3y = 9 in slope-intercept form.

Solution

This equation is in standard form. Perform the necessary steps to solve the equation for y.

 6x + 3y = 9 6x + 3y - 6x = 9 - 6x Subtract 6x from each side. 3y = -6x + 9 y = -2x + 3 Divide each side by 3.

This equation is in slope-intercept form, with a slope of - 2 and a y-intercept of 3.

Key Idea

To convert from standard form to slope-intercept form,

• move the x term to the right-hand side of the equation, and

• divide each side by the coefficient of y.

These steps for converting from standard form to slope-intercept form work whenever the coefficient of y is not zero. If it is zero, the line is vertical and the slope is undefined.

Example 2

Write 7( y - 3) = 28( x + 2) in slope-intercept form.

Solution

To do this, first multiply through all the terms within parentheses using the Distributive Property.

 7( y - 3) = 28( x + 2) 7y - 21 = 28x + 56 Distributive Property 7y - 21 + 21 = 28x + 56 + 21 Add 21 to each side. 7y = 28 x + 77 y = 4x + 11 Divide each side by 7.

This is the slope-intercept form of the equation. The slope is 4 and the y-intercept is 11.

Key Idea

To convert from point-slope form to slope-intercept form,

• use the Distributive Property to multiply through all expressions in parentheses,

• remove the constant from the left-hand side, and

• divide each side by the coefficient of y.