Slope and y-intercepts Practice
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Question
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 on both ends passes through the following closed points: left parenthesis 0 comma 0 right parenthesis and left parenthesis 2 comma 3 right parenthesis.
Determine the initial value and the rate of change of the linear function given in the graph.
(1 point)
The initial value is
, and the rate of change is
.
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To determine the initial value, we can simply read off the y-intercept, which is the point where the line intersects the y-axis. In this case, the y-intercept is (0,0), so the initial value is 0.
To determine the rate of change, we can calculate the slope of the line. The slope is calculated using the formula:
slope = (change in y) / (change in x)
In this case, the change in y is 3 (going from y=0 to y=3) and the change in x is 2 (going from x=0 to x=2). Therefore, the slope is:
slope = 3/2 = 1.5
So, the initial value is 0 and the rate of change is 1.5.