The points on the graph are (2.6,-6) and (3.2,3) Determan the initial value and rate change

1 answer

To find the initial value and rate of change, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where m is the rate of change (also known as the slope) and b is the initial value (also known as the y-intercept).

First, let's find the rate of change (m). The formula for finding the slope between two points is:

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

Using the given points (2.6, -6) and (3.2, 3):

m = (3 - (-6)) / (3.2 - 2.6)
m = 9 / 0.6
m = 15

So, the rate of change is 15.

Next, let's use one of the given points, (2.6, -6), to find the initial value (b). We'll substitute the coordinates (x = 2.6, y = -6) into the slope-intercept form of the equation:

-6 = 15(2.6) + b
-6 = 39 + b
b = -6 - 39
b = -45

Therefore, the initial value is -45.

In summary:
The rate of change is 15.
The initial value is -45.