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.
The initial value is
, and the rate of change is
.
To determine the initial value of the linear function, we can look at the y-intercept, which is where the line crosses the y-axis. From the points given, we can see that the line crosses the y-axis at (0, 1). Therefore, the initial value of the linear function is 1.
To determine the rate of change of the linear function, we can calculate the slope of the line. The slope is calculated using the formula:
slope = (change in y) / (change in x)
From the points given, we can calculate the slope between each pair of points:
Slope between (-3, 2.5) and (0, 1):
slope = (1 - 2.5) / (0 - (-3))
slope = (-1.5) / (3)
slope = -0.5
Slope between (0, 1) and (2, 0):
slope = (0 - 1) / (2 - 0)
slope = (-1) / (2)
slope = -0.5
Since the slope between each pair of points is the same (-0.5), we can conclude that the rate of change of the linear function is -0.5.
Therefore, the initial value of the linear function is 1, and the rate of change is -0.5.