In order for the data in the table to represent a linear function
with a rate of change of 8, what must be the value of a?
a= 2
a=3
a = 19
a = 35

We know the slope, or rate of change, is -8 because y decreases as x increases, and so we are looking for the y-intercept. This will help us to find a.

y = -8x + b

11 = -8(12) + b

11 = -96 + b

b = 107

y = -8x + 107

Now that we have our equation, we can plug in 11 for x and solve for y.

y = -8(11) + 107

y = -88 + 107

y = 19

The value of a is 19.

Hope this helps!! :)

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.