To determine the initial value and rate of change of the linear function, we can use the formula for the equation of a line: y = mx + b, where m represents the rate of change and b represents the initial value (or y-intercept).
Looking at the given points (-3, 4), (0, 3), (3, 2), and (6, 1), we can calculate the rate of change (m) by finding the difference in y-coordinates and dividing by the difference in x-coordinates:
m = (change in y) / (change in x)
For the points (-3, 4) and (0, 3):
change in y = 3 - 4 = -1
change in x = 0 - (-3) = 3
m = -1/3
Now we can substitute the values of one of the points into the equation y = mx + b to solve for b:
Using the point (0, 3):
3 = (-1/3)(0) + b
3 = b
So the initial value (b) is 3.
Therefore, the linear function can be written as y = -1/3x + 3.
The initial value is 3 and the rate of change is -1/3.
Use the image to answer the question.
An illustration of a coordinate plane with four quadrants shows the x and y axes extending from -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: (-3, 4), (0, 3), (3, 2), and (6, 1).
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 answer