To graph a linear function using the x and y intercepts for the equation \(2x + 4y = 12\), we need to find the points where the line intersects the x-axis and the y-axis.
**Step 1:** Finding the x-intercept (where the line crosses the x-axis).
To find the x-intercept, set \(y = 0\) in the equation and solve for \(x\):
\[2x + 4(0) = 12\]
\[2x = 12\]
\[x = 6\]
So, the x-intercept is at the point (6, 0).
**Step 2:** Finding the y-intercept (where the line crosses the y-axis).
To find the y-intercept, set \(x = 0\) in the equation and solve for \(y\):
\[2(0) + 4y = 12\]
\[4y = 12\]
\[y = 3\]
So, the y-intercept is at the point (0, 3).
Now, we can plot these points on the coordinate plane and draw the line passing through them.
Here's the graph:
```
|
| *
| *
| *
| *
| *
|______________________________
6 0 3
```
The line passes through the points (6, 0) and (0, 3).
