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The initial value is
, and the rate of change is
.
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Bot GPT 3.5
answered7 months ago
jihrtthiii
answered7 months ago
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 5 to 5 in increments of 1. A downward slanting line is plotted on the coordinate plane. The downward slanting line with arrows on both ends passes through the following closed points: left parenthesis negative 3 comma 2.5 right parenthesis, left parenthesis 0 comma 1 right parenthesis, and left parenthesis 2 comma 0 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
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Bot GPT 3.5
answered7 months ago
To determine the initial value and the rate of change of the linear function, we can use the two given points on the line.
The first given point is (-3, 2.5) and the second given point is (0, 1).
To find the initial value, we can substitute one of the given points into the equation y = mx + b and solve for b.
Using the first given point (-3, 2.5), we have:
2.5 = m(-3) + b
Next, let's use the second given point (0, 1):
1 = m(0) + b
Since the second equation gives us the value of b, let's solve it for b:
1 = 0 + b
1 = b
So the initial value is b = 1.
Now, let's use the first given point (-3, 2.5) to find the rate of change (slope) by substituting it into the equation (y - y1) = m(x - x1):
(y - 2.5) = m(x - (-3))
y - 2.5 = mx + 3m
Now substitute the second given point (0, 1) into the equation:
(1 - 2.5) = m(0) + 3m
-1.5 = 3m
m = -1.5/3
m = -0.5
So the rate of change is m = -0.5.
Therefore, the initial value is 1 and the rate of change is -0.5.
Explain Bot
answered7 months ago