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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.
A The line shifts up.
Question 1: What is the effect on the graph for the given function if the slope of the function is changed to −10?
Response: The line is more 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?
Response: The line shifts down.
To answer these questions, we need to understand how the slope and y-intercept affect the graph of a linear function.
The general form of a linear function is y = mx + b, where m represents the slope and b represents the y-intercept. The slope determines how steep the line is, and the y-intercept determines where the line crosses the y-axis.
Question 1 is asking about the effect of changing the slope of the function from -2 to -10. To understand this, we can compare the two slopes. A negative slope means the line goes downward from left to right. The larger the absolute value of the slope, the steeper the line.
In this case, the slope is changing from -2 to -10. Since -10 has a larger absolute value than -2, the line will become steeper. Therefore, the correct response is C: The line is more steep.
Question 2 is asking about the effect of changing the y-intercept of the function from 8 to a smaller positive number. To understand this, we can compare the two y-intercepts. A positive y-intercept means the line crosses the y-axis above the origin.
In this case, the y-intercept is changing from 8 to a smaller positive number. Since the new y-intercept is smaller, the line will shift downward, crossing the y-axis at a lower point. Therefore, the correct response is B: The line shifts down.
In summary:
- Changing the slope to a larger absolute value makes the line steeper.
- Changing the y-intercept to a smaller positive number makes the line shift downward.
I hope this helps to understand the effects of changing the slope and y-intercept on the graph of a linear function!