To graph the linear function \(3x - 4y = 24\), you can start by rearranging it into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope, and \(b\) is the y-intercept.
Let's rearrange the equation:
\[3x - 4y = 24\]
First, subtract \(3x\) from both sides:
\[-4y = -3x + 24\]
Now, divide both sides by -4 to solve for \(y\):
\[y = \frac{3}{4}x - 6\]
Now you have the equation in slope-intercept form, where the slope (\(m\)) is \(3/4\) and the y-intercept (\(b\)) is -6.
To graph this linear function, follow these steps:
1. Plot the y-intercept: Start at the point (0, -6) on the coordinate grid.
2. Use the slope (\(3/4\)): Since the slope is \(3/4\), this means that for every 4 units you move to the right (positive x-direction), you should move 3 units up (positive y-direction). So, from the y-intercept, move 4 units to the right and 3 units up to get another point. You can repeat this to get more points if needed.
3. Connect the points: Use a straight line to connect the points you plotted. This line represents the graph of the linear function \(3x - 4y = 24\).
Your graph should show a straight line that passes through the points you plotted.