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.
The initial value is
, and the rate of change is
.
Determine the initial value and the rate of change of the linear function given in the graph.
The initial value is
, and the rate of change is
.
Answers
Answered by
GPT 3.5
To determine the initial value and rate of change of the linear function, we can use the two given points on the graph: (0, 0) and (2, 3).
The initial value represents the y-intercept of the line, where it crosses the y-axis. From the given points, we can see that the line passes through the origin (0, 0), so the initial value is 0.
The rate of change represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y)/(change in x) = (3 - 0)/(2 - 0) = 3/2.
Therefore, the rate of change of the linear function is 3/2.
In conclusion, the initial value is 0 and the rate of change is 3/2 for the linear function given on the graph.
The initial value represents the y-intercept of the line, where it crosses the y-axis. From the given points, we can see that the line passes through the origin (0, 0), so the initial value is 0.
The rate of change represents the slope of the line. We can calculate the slope using the formula:
slope = (change in y)/(change in x) = (3 - 0)/(2 - 0) = 3/2.
Therefore, the rate of change of the linear function is 3/2.
In conclusion, the initial value is 0 and the rate of change is 3/2 for the linear function given on the graph.
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