Question

Find the slope and y-intercept of this line and graph it: 3x+2y=6.

Answer 1

Write the equation in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

The equation is 3x + 2y = 6.

Subtract 3x from each side.

3x + 2y - 3x = 6 - 3x

Group like terms.

2y = 6 - 3x

Divide each side by 2.

y = (6 - 3x)/2

y = (- 3/2)x + 3.

Compare the equation with slope-intercept form y = mx + b.

slope = - 3/2 and y-intercept is 3.

y-intercept is 3, so the line crosses the y-axis at (0, 3)

Using slope find the next point.

Slope = rise/run = -3/2

Start at point (0, 3), move 3 units down and 2 units right, then plot the point (2, 0).

Draw a line through these points.

Graph :

Answer 2

Write the equations in slope-intercept form y = mx + b, where m is slope and b is y-intercept.

The equation is3x + 2y = 6.

Subtract 3x from each side.

2y = 6 - 3x

Divide each side by 2.

y = (- 3/2)x + 3.

Compare the equation with slope-intercept form y = mx + b.

slope = - 3/2 and y-intercept is 3.

y-intercept is 3, so the line crosses the y-axis at (0, 3)

Using slope find the next point.

Slope = rise/run = - 3/2

Start at point (0, 3), move 3 units down and 2 units right, then plot the point (2, 0).

Graph :