A line in the xy-plane has the equation 3y - 2x = 12. What is the slope of this line? — SAT

A line in the $xy$ -plane has the equation $3y - 2x = 12$ . What is the slope of this line?

The slope of the line is

\frac{2}{3}

To find the slope, the equation

3y - 2x = 12

is rewritten in slope-intercept form (

y = mx + b

). Adding

2x

to both sides gives

3y = 2x + 12

. Dividing by

3

yields

y = \frac{2}{3}x + 4

. The slope is the coefficient of

x

, which is

\frac{2}{3}

Isolate the term containing

y

by adding

2x

to both sides of the equation.

3y = 2x + 12

To express the equation in slope-intercept form (

y = mx + b

Divide all terms in the equation by

3

to solve for

y

y = \frac{2}{3}x + 4

To isolate

y

and identify the slope,

m

, which is the coefficient of

x

Finding the slope of a line from its linear equation by rewriting it in slope-intercept form.

Question