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. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 1.5 comma negative 3 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 0.5 comma 1 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point)
Responses
The initial value is 0, and the rate of change is 2.
The initial value is 0, and the rate of change is 2.
The initial value is −6, and the rate of change is 2.
The initial value is negative 6 , and the rate of change is 2.
The initial value is 0, and the rate of change is 1/2.
The initial value is 0, and the rate of change is Start Fraction 1 over 2 End Fraction.
The initial value is 2, and the rate of change is 2.
The initial value is 2, and the rate of change is 2.
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The correct answer is:
The initial value is 0, and the rate of change is 2.
you sure?
Apologies for the confusion. Let's analyze the points on the line: (-1.5, -3), (0, 0), and (0.5, 1).
To find the rate of change, we can calculate the slope of the line using the formula:
slope = (change in y) / (change in x)
The change in y between the two points (-1.5, -3) and (0, 0) is 0 - (-3) = 3. The change in x is 0 - (-1.5) = 1.5. So the slope between these two points is:
slope = (3) / (1.5) = 2
Therefore, the rate of change is 2.
To find the initial value, we can substitute the coordinates of any of the points (0, 0) or (0.5, 1) into the equation of the line, y = mx + b, and solve for b.
Using the point (0, 0), we have:
0 = 2(0) + b
0 = 0 + b
b = 0
Therefore, the initial value or y-intercept is 0.
So, the correct answer is:
The initial value is 0, and the rate of change is 2.