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The problem asks to solve a system of equations graphically. The system is:

1. \( y = \frac{4}{5}x + 8 \)
2. \( 2x + y = -6 \)

### Step-by-step process to graph the equations:

#### 1. Graph the first equation: \( y = \frac{4}{5}x + 8 \)
   - This is a straight line in slope-intercept form (\( y = mx + b \)), where the slope \( m = \frac{4}{5} \) and the y-intercept \( b = 8 \).
   - Start at \( (0, 8) \) on the y-axis.
   - Use the slope \( \frac{4}{5} \) to plot another point. From \( (0, 8) \), move 5 units to the right and 4 units up to get another point at \( (5, 12) \).

#### 2. Rewrite the second equation in slope-intercept form:
   \( 2x + y = -6 \) can be rearranged to solve for \( y \):
   \[
   y = -2x - 6
   \]
   - Here, the slope \( m = -2 \) and the y-intercept \( b = -6 \).
   - Start at \( (0, -6) \) on the y-axis.
   - Use the slope \( -2 \), which means for every 1 unit you move to the right, you go 2 units down. Plot another point at \( (1, -8) \).

#### 3. Graph both lines and find the intersection:
   - The intersection of these two lines represents the solution to the system of equations.

Since your current graph shows one of the lines plotted, you would need to plot the second one and find the intersection point to solve the system. The solution is the \( (x, y) \)-coordinates where the two lines meet.

Would you like further details or to explore this solution more?

### Follow-up questions:
1. What is the algebraic solution of the system using substitution or elimination?
2. How do you determine the slope from a given equation?
3. What does the intersection point of two lines represent in terms of the system of equations?
4. How do you convert an equation from standard form to slope-intercept form?
5. How would the graph look if the slopes of both lines were equal?

### Tip:
Always check the intersection of two lines carefully to ensure accuracy when solving graphically.

Solve the following system of equations graphically: y = (4/5)x + 8 and 2x + y = -6.

Learn how to solve the system of linear equations y = (4/5)x + 8 and 2x + y = -6 by graphing. This detailed solution explains the graphing process, the use of slope-intercept form, and how to find the intersection point to determine the solution.

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