Question

se the table to answer the question.

x y
1 4
−3 8
Find the rate of change and the initial value of the linear function given as a table of values.

(1 point)
The rate of change is m=
, and the initial value is b=

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change, we can use the formula for the slope of a linear function:

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

Using the values from the table:

m = (8 - 4)/(-3 - 1)
m = 4/-4
m = -1

So, the rate of change is -1.

To find the initial value (y-intercept), we can plug one of the points into the formula for a linear function:

y = mx + b

Using the point (1,4):

4 = -1(1) + b
4 = -1 + b
b = 5

So, the initial value is 5.

Answer 2

Whats the rate change

Answer 3

[AI-generated answer — Bot GPT 3.5]

The rate of change is -1.

Answer 4

Determine the initial value and the rate of change of the linear function given in the graph.

(1 point)
The initial value is
, and the rate of change is
.

Answer 5

[AI-generated answer — Bot GPT 3.5]

I'm sorry, but I cannot see the graph. Could you please provide me with the values of two points from the graph, so I can calculate the initial value and rate of change using the formula for the slope of a linear function and the y-intercept?

Answer 6

The y intercept is 0, 0

Answer 7

[AI-generated answer — Bot GPT 3.5]

If the y-intercept is at (0,0), then the initial value (y-intercept) is 0.

The rate of change can be determined by selecting another point on the line to calculate the slope (rate of change).

Let's choose another point (x, y) on the line for calculation. Could you provide another point on the line?

Answer 8

2, 3

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the rate of change (slope), we can use the formula:

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

Using the points (0,0) and (2,3):

m = (3 - 0)/(2 - 0)
m = 3/2
m = 1.5

Therefore, the rate of change (slope) is 1.5.

Given:
Initial value (y-intercept): 0
Rate of change (slope): 1.5

Answer 10

Same question but with the coords of 0,1 for y intercept and 2,0 for the other one

Answer 11

[AI-generated answer — Bot GPT 3.5]

Using the points (0,1) and (2,0) to calculate the rate of change (slope):

m = (y2 - y1)/(x2 - x1)
m = (0 - 1)/(2 - 0)
m = -1/2
m = -0.5

Therefore, the rate of change (slope) is -0.5 when the y-intercept is at (0,1).

Answer 12

Whats the inital value and whats the rate of change

Answer 13

[AI-generated answer — Bot GPT 3.5]

Given:

Initial value (y-intercept): 1
Rate of change (slope): -0.5