Asked by Eli S
x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.
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Answered by
GPT 3.5
To find the rate of change and the initial value of the linear function, we need to determine the slope and y-intercept of the line that passes through the given points.
Using the slope formula:
slope = (change in y) / (change in x) = (8 - 4) / (-3 - 1) = 4 / -4 = -1
Therefore, the rate of change of the linear function is -1.
To find the initial value (y-intercept), we can use one of the given points. Let's use the point (1, 4).
Using the equation of a line (y = mx + b) and substituting the values:
4 = -1(1) + b
Simplifying the equation:
4 = -1 + b
4 + 1 = b
b = 5
Therefore, the initial value (y-intercept) of the linear function is 5.
The linear function is y = -x + 5.
Using the slope formula:
slope = (change in y) / (change in x) = (8 - 4) / (-3 - 1) = 4 / -4 = -1
Therefore, the rate of change of the linear function is -1.
To find the initial value (y-intercept), we can use one of the given points. Let's use the point (1, 4).
Using the equation of a line (y = mx + b) and substituting the values:
4 = -1(1) + b
Simplifying the equation:
4 = -1 + b
4 + 1 = b
b = 5
Therefore, the initial value (y-intercept) of the linear function is 5.
The linear function is y = -x + 5.
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