The uploaded image shows a question about solving systems of equations graphically, with one graph provided and multiple-choice options for the equation of a second line (question 4). It also includes a system of equations to solve graphically in question 5. Let’s analyze question 4 first.

Question 4 Analysis:

The graph shows two intersecting lines, with the solution to the system given as the point $(2, -7)$. To find which equation could represent the second line, substitute $(2, -7)$ into each equation from the options:

1. Option A: $y = -\frac{1}{2}x - 8$ Substitute $x = 2, y = -7$: $-7 = -\frac{1}{2}(2) - 8 \implies -7 = -1 - 8 \implies -7 \neq -9$ This is incorrect.

2. Option B: $y = \frac{3}{2}x + 3$ Substitute $x = 2, y = -7$: $-7 = \frac{3}{2}(2) + 3 \implies -7 = 3 + 3 \implies -7 \neq 6$ This is incorrect.

3. Option C: $y = -2x + 3$ Substitute $x = 2, y = -7$: $-7 = -2(2) + 3 \implies -7 = -4 + 3 \implies -7 \neq -1$ This is incorrect.

4. Option D: $y = x - 8$ Substitute $x = 2, y = -7$: $-7 = 2 - 8 \implies -7 = -7$ This is correct.

Thus, the answer for question 4 is D.

Do you want me to proceed with analyzing question 5 in the image? Let me know!

Relative Questions to Expand Learning:

1. How do you determine the point of intersection of two lines algebraically?
2. What does "infinitely many solutions" mean for a system of equations?
3. How can we confirm the slope of a line from its equation?
4. What is the importance of graphing systems of equations in real-world scenarios?
5. How can substitution be used to verify solutions to systems of equations?

Tip:

Always double-check calculations when substituting values into equations to avoid simple arithmetic errors.