To determine the initial value, we can use one of the points given in the graph. Let's use the point (-3, 4). The initial value is the y-intercept, which is the value of y when x = 0.
Using the point (-3, 4), we have:
y = mx + b
4 = m(-3) + b
4 = -3m + b
Next, let's use the point (0, 3) to find the rate of change (slope). The rate of change is the change in y over the change in x between two points on the line.
Using the points (-3, 4) and (0, 3), we have:
m = (y2 - y1) / (x2 - x1)
m = (3 - 4) / (0 - (-3))
m = -1 / 3
Substitute m = -1/3 into the equation 4 = -3m + b:
4 = -3(-1/3) + b
4 = 1 + b
b = 3
Therefore, the initial value is 3, and the rate of change is -1/3.
Functions Unit Test....
6 of 156 of 15 Items
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. 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 4 right parenthesis, left parenthesis 0 comma 3 right parenthesis, left parenthesis 3 comma 2 right parenthesis, and left parenthesis 6 comma 1 right parenthesis.
Determine the initial value and the rate of change of the linear function as given in the graph. Round the answer to three decimal places as needed.
(1 point)
The initial value is
, and the rate of change is
.
1 answer