To solve this problem, we need to determine the rates of increase (slopes) of both Line A and Line B and compare them.

Step 1: Rate of increase (slope) of Line A

The slope of Line A is the coefficient of $x$ in its equation, $y = 5x - 7$.

• Slope of Line A = $5$.

Step 2: Rate of increase (slope) of Line B

To find the slope of Line B, we use the formula for the slope between two points, $(x_1, y_1)$ and $(x_2, y_2)$:
$\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(-1, -4)$ and $(1, 7)$:
$\text{slope} = \frac{7 - (-4)}{1 - (-1)} = \frac{7 + 4}{1 + 1} = \frac{11}{2} = 5.5$

Step 3: Compare the slopes

• Slope of Line A = $5$
• Slope of Line B = $5.5$

Since $5.5 > 5$, Line B has the greater rate of increase.

Final Answer:

Select Line B.

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Would you like further clarification? Here are some related questions to deepen understanding:

1. What does the slope of a line represent in a real-world scenario?
2. How do you determine the slope if only a graph is provided?
3. How would the answer change if Line A had a slope of $6$?
4. What happens to the slope of a line if you flip its direction on a graph?
5. Can two different lines ever have the same slope? If so, what does that mean?

Tip: Always pay close attention to the slope of a line when analyzing its rate of increase—it's the key to understanding how steeply it rises or falls!