Final answer:
To graph the equation 12x - 9y = 36, rearrange it to solve for y in terms of x. The equation y = (4/3)x - 4 represents the line. Plot the y-intercept and use the slope to determine additional points to graph the line.
Step-by-step explanation:
To graph the equation 12x - 9y = 36, we can rearrange it to solve for y in terms of x. First, subtract 12x from both sides of the equation, which gives -9y = -12x + 36. Then, divide both sides by -9 to isolate y, giving y = (4/3)x - 4.
This equation is in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope is 4/3 and the y-intercept is -4.
Using this information, plot the y-intercept at (0, -4) on the coordinate plane and use the slope to determine additional points to plot. The slope of 4/3 means that for every 3 units moved to the right, we move up 4 units. Once you have enough points plotted, draw a straight line connecting them to graph the equation.
Learn more about Graphing Linear Equations