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To solve the given system of equations by graphing, we have the following equations:

1. \( y = -\frac{7}{4}x + 7 \)
2. \( 7x - 8y = 112 \)

### Step 1: Graph the first equation

The first equation is already in slope-intercept form (\( y = mx + b \)), where:
- Slope \( m = -\frac{7}{4} \)
- y-intercept \( b = 7 \)

You can plot this by starting at \( (0, 7) \) on the y-axis and using the slope to find other points. Since the slope is \( -\frac{7}{4} \), move 4 units to the right and 7 units down for the next point.

### Step 2: Rewrite the second equation

We need to express the second equation in slope-intercept form as well. Start with:
\[
7x - 8y = 112
\]

Solve for \( y \):
\[
-8y = -7x + 112
\]
\[
y = \frac{7}{8}x - 14
\]

Now, we have the second equation in slope-intercept form:
\[
y = \frac{7}{8}x - 14
\]
This gives:
- Slope \( m = \frac{7}{8} \)
- y-intercept \( b = -14 \)

Start at \( (0, -14) \) on the y-axis, and use the slope \( \frac{7}{8} \) to find more points: move 8 units to the right and 7 units up for another point.

### Step 3: Find the intersection

The solution to the system of equations is the point where the two lines intersect. To find the exact solution algebraically, set the two equations equal to each other:
\[
-\frac{7}{4}x + 7 = \frac{7}{8}x - 14
\]

Solve this equation for \( x \):
\[
-\frac{7}{4}x - \frac{7}{8}x = -14 - 7
\]
\[
-\frac{14}{8}x - \frac{7}{8}x = -21
\]
\[
-\frac{21}{8}x = -21
\]
\[
x = 8
\]

Now, substitute \( x = 8 \) back into one of the original equations (we'll use \( y = -\frac{7}{4}x + 7 \)) to find \( y \):
\[
y = -\frac{7}{4}(8) + 7
\]
\[
y = -14 + 7 = -7
\]

Thus, the solution is \( x = 8 \), \( y = -7 \).

### Conclusion
The lines intersect at the point \( (8, -7) \), which is the solution to the system.

Would you like further details on the graphing process or any other clarification?

### Related Questions:
1. How do you graph a line given its slope and y-intercept?
2. What are some common methods to solve systems of equations besides graphing?
3. How can you check if your graphical solution is correct?
4. How do you convert a standard form equation to slope-intercept form?
5. What is the significance of the slope in the context of graphing?

### Tip:
When graphing lines, always plot at least two points to ensure accuracy.

Solve the system of equations by graphing: y = -7/4x + 7 and 7x - 8y = 112.

Solve the system of equations y = -7/4x + 7 and 7x - 8y = 112 by graphing. Learn the step-by-step method, including rewriting equations into slope-intercept form, plotting points, and finding the intersection. Suitable for students in Grades 8-10.

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