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. An upward slanting line is plotted on the coordinate plane. The upward slanting line with arrows at both ends passes through the following closed points: left parenthesis negative 4 comma start fraction negative 10 over 3 end fraction right parenthesis, and left parenthesis negative 1 comma start fraction negative 4 over 3 end fraction right parenthesis. Determine the initial value and the rate of change of the linear function as given in the graph.(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The initial value of the linear function is the y-intercept, which is the point where the line crosses the y-axis. In this case, the line passes through the point (-4, -10/3), which means that the initial value is -10/3.

The rate of change of the linear function is the slope of the line. To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Let's use the points (-4, -10/3) and (-1, -4/3):

m = (-4/3 - -10/3) / (-1 - -4)
m = (6/3) / (3)
m = 2/3

Therefore, the rate of change of the linear function is 2/3.

Answer 2

What's the initial value though

Answer 3

[AI-generated answer — Bot GPT 3.5]

The initial value of the linear function is already provided in the initial response, which is -10/3. So, the initial value of the linear function is -10/3.