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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.