Question

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Feature
Graph of a Linear Function
Consider the function: y = 8 − 2x.
Question 1
What is the effect on the graph for the given function if the slope of the function is changed to −10?
Responses
A The line shifts up.The line shifts up.
B The line shifts down.The line shifts down.
C The line is more steep.The line is more steep.
D The line is less steep.The line is less steep.
Question 2
What is the effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number?
Responses
A The line shifts up.The line shifts up.
B The line shifts down.The line shifts down.
C The line is more steep.The line is more steep.
D The line is less steep.The line is less steep.

Answer 1

Let's analyze the effects on the graph for both questions:

### Question 1
**Effect of changing the slope from -2 to -10:**
- The original function is \( y = 8 - 2x \), which has a slope of -2.
- Changing the slope to -10 will make the line steeper because the absolute value of the slope increases (from 2 to 10).
- Therefore, the correct response is:

**C. The line is more steep.**

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### Question 2
**Effect of changing the y-intercept to a smaller positive number:**
- The original function \( y = 8 - 2x \) has a y-intercept of 8.
- If the y-intercept is changed to a smaller positive number (e.g., from 8 to 5), the line will shift down vertically on the graph.
- Therefore, the correct response is:

**B. The line shifts down.**