Write the equation in slope-intercept form. Then find the slope and the  y-intercept of th...

Write the equation in slope-intercept form. Then find the slope and the  y-intercept of the line determined by the equation.See Example.

EXAMPLE Find the slope and the y-intercept of the line with the equation 2x + 3y =-9. Then graph the line.

Strategy We will solve the equation for y to write the equation in slope-intercept form (y = mx + b). Then we will plot the y-intercept, and use the slope to determine a second point on the line.

WHY Once we locate two points on the line, we can draw the graph of the line.

Solution

We write an equation in the form y = mx + b to find the slope m and the y-intercept (0, b).

The slope of the line is , which can be expressed as . After plotting the y-intercept, (0, -3), we move 2 units downward (rise) and then 3 units to the right (run). to locate a third point on the line, (3, -5). From this point, we move another 2 units downward and 3 units to the right to locate a third point on the line, (6, -7). Then we draw a line through the points to obtain the graph shown in the figure.

5(2x − 3y) = 4