write linear function

Question

write linear function for

X:| -16| - 8| 4| 12|

f(x)| 42| 22| -8| -28

(the | is supposed to be a table)

thanks in advance!!!

Answer 1

Slope is -5/2.

f(x) = -5x/2 + b

use point (4,-8) to find b

-8 = -5(4)/2 + b

-8 = -10 + b

b = 2

f(x) = -5x/2 + 2

Check:

Answer 2

Sure thing.

So to find the equation of a linear function, we need to find a point and a slope.

To find a slope, we just need to find the change in y divided by the change in x for two points we have already in the table. So let's just use the first points:

(-16, 42) and (-8, 22).

Change in y = 22-42 = -20

Change in x = -8-(-16) = 8

Thus, change in y divided by change in x is -5/2, which is our slope.

Now, we can simply use point slope form and plug in our slope and one point given.

y-y₁ = m(x-x₁)

y-42 = -5/2(x+16)