https://file.aiquickdraw.com/mathbot/file/1729373371995k47j4xee.jpg

The equation given in the image is:

\[
0.5x - 4y = 12
\]

To graph this equation, it is easier to rewrite it in slope-intercept form, \( y = mx + b \), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Solve for \(y\)
We start by isolating \(y\):

\[
0.5x - 4y = 12
\]
Subtract \(0.5x\) from both sides:
\[
-4y = -0.5x + 12
\]
Now, divide both sides by \(-4\):
\[
y = \frac{-0.5x + 12}{-4}
\]
This simplifies to:
\[
y = \frac{0.5}{4}x - \frac{12}{4}
\]
\[
y = \frac{1}{8}x - 3
\]

### Step 2: Interpret the slope and y-intercept
Now we have the equation:
\[
y = \frac{1}{8}x - 3
\]
- The slope \(m = \frac{1}{8}\) means that for every 8 units you move horizontally to the right, you move 1 unit vertically up.
- The y-intercept \(b = -3\) means the line crosses the y-axis at \( (0, -3) \).

### Step 3: Plot the line
- Start by plotting the point \( (0, -3) \) on the y-axis.
- From this point, use the slope \( \frac{1}{8} \): move 8 units to the right and 1 unit up to find another point on the line.
- Draw the line through these points.

Would you like further details on how to find specific points on the graph, or do you have any other questions?

Here are 5 questions that can help expand on this concept:
1. How do you calculate the x-intercept of the equation?
2. How can you verify the slope from a graph?
3. What does it mean when the slope is positive or negative?
4. How would you graph this equation if the slope were steeper, such as \(y = 2x - 3\)?
5. What are other forms of linear equations besides slope-intercept form?

**Tip:** Always double-check the y-intercept when rewriting equations into slope-intercept form to ensure accuracy when graphing.

The graph of 0.5x - 4y = 12 is shown on the grid.

Learn how to graph the linear equation 0.5x - 4y = 12 by rewriting it in slope-intercept form. This problem covers key algebraic concepts, including slope, y-intercept, and graphing techniques, suitable for students in Grades 8-10.

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