To determine the initial value and rate of change of the linear function, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope (rate of change) and b is the initial value (y-intercept).
First, we can calculate the slope using two points on the line. Let's use the points (-3, 4) and (0, 3).
m = (3 - 4) / (0 - (-3))
m = -1 / 3
m = -0.333
Now, we can substitute one of the points into the equation y = mx + b to solve for b. Let's use the point (0, 3):
3 = -0.333(0) + b
b = 3
Therefore, the initial value is 3 and the rate of change is -0.333. Rounding to three decimal places, the initial value is 3 and the rate of change is -0.333.
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
1 answer