Question
Determine the rate of change and the initial value of the linear function given here as a table of values.
(1 point)
Responses
m=−7, b=−3
m=−7, b=−3
m=−3, b=−7
m=−3, b=−7
m=−0.5, b=5.5
m=−0.5, b=5.5
m=−0.5, b=10.5
m=−0.5, b=10.5
(1 point)
Responses
m=−7, b=−3
m=−7, b=−3
m=−3, b=−7
m=−3, b=−7
m=−0.5, b=5.5
m=−0.5, b=5.5
m=−0.5, b=10.5
m=−0.5, b=10.5
Answers
Answered by
GPT-4o mini
To determine the rate of change (slope, \( m \)) and the initial value (y-intercept, \( b \)) of a linear function from a table of values, we need to analyze how the values change as the input (typically \( x \)) changes.
However, since you did not provide the specific table of values, I'll explain how to compute the slope and y-intercept:
1. **Finding the Slope \( m \)**: The slope of a linear function can be calculated using the formula:
\[
m = \frac{\Delta y}{\Delta x}
\]
where \( \Delta y \) is the change in \( y \) values and \( \Delta x \) is the change in \( x \) values between two points on the line.
2. **Finding the Y-Intercept \( b \)**: The y-intercept is the value of \( y \) when \( x = 0 \). You can identify this from the table if it provides a value for \( x = 0 \), or you can rearrange the linear equation (once you have the slope) to find \( b \).
If you provide that actual table of values, I can help you to compute the precise values of \( m \) and \( b \). Please share the table for a more precise analysis! Alternatively, based on the options given, if you remember any values from your table, indicate whether they correspond to any of the options listed.
However, since you did not provide the specific table of values, I'll explain how to compute the slope and y-intercept:
1. **Finding the Slope \( m \)**: The slope of a linear function can be calculated using the formula:
\[
m = \frac{\Delta y}{\Delta x}
\]
where \( \Delta y \) is the change in \( y \) values and \( \Delta x \) is the change in \( x \) values between two points on the line.
2. **Finding the Y-Intercept \( b \)**: The y-intercept is the value of \( y \) when \( x = 0 \). You can identify this from the table if it provides a value for \( x = 0 \), or you can rearrange the linear equation (once you have the slope) to find \( b \).
If you provide that actual table of values, I can help you to compute the precise values of \( m \) and \( b \). Please share the table for a more precise analysis! Alternatively, based on the options given, if you remember any values from your table, indicate whether they correspond to any of the options listed.