Let me extract the problem from the image and help solve it.

The problem asks to match the equations or line descriptions on the left with the correct slope values on the right. Let's analyze them one by one.

1. Equation: $x = -3$

• This represents a vertical line where all points have $x = -3$, and the slope of a vertical line is undefined.

2. Equation: $6x - 3y = 18$

• Rewrite in slope-intercept form ($y = mx + b$): $6x - 3y = 18 \quad \Rightarrow \quad -3y = -6x + 18 \quad \Rightarrow \quad y = 2x - 6$
• Here, the slope ($m$) is 2.

3. Line passing through points $(7, 5)$ and $(8, 5)$

• Use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 5}{8 - 7} = \frac{0}{1} = 0$
• The slope is 0.

4. Line passing through points $(4, -2)$ and $(1, 7)$

• Use the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - (-2)}{1 - 4} = \frac{9}{-3} = -3$
• The slope is -3.

Final Matches:

1. $x = -3$ → Undefined
2. $6x - 3y = 18$ → 2
3. Line through $(7, 5)$ and $(8, 5)$ → 0
4. Line through $(4, -2)$ and $(1, 7)$ → -3

Would you like further clarification or detailed explanations?

5 Follow-Up Questions:

1. How do you calculate the slope of a vertical or horizontal line?
2. What does the slope-intercept form ($y = mx + b$) tell us about a line?
3. How can you identify if a slope is positive, negative, zero, or undefined from a graph?
4. Can all linear equations be converted to slope-intercept form?
5. How does the slope formula work when both points are on the same vertical line?

Tip:

Always simplify the equation to slope-intercept form ($y = mx + b$) when possible to find the slope easily!