Question

find the linear function f(x) for which both f(-2) and f(0)=-4

Answer 1

If you have a linear function that has 2 x values produce the same y value, then this function must graph a horizontal line.

Answer 2

it's f(-2)=6, sorry

Answer 3

oh nvm

Answer 4

are you able to find the slope through the two points (-2,6) and (0,-4) ?

Answer 5

How do I come up with that?

Answer 6

are you familiar with the slope formula?

Answer 7

It's y=mx+b right?

Answer 8

that's slope intercept form, which is close to what I'm referring to

Answer 9

I'm actually talking about this formula

\[\Large m = \frac{y_2-y_1}{x_2-x_1}\]

Answer 10

I don't know which one to plug which into. I think that's my problem.

Answer 11

Basically you find the y difference by subtracting the y coordinates

Do the same for the x coordinates (in the same order)

then you divide the y difference by the x difference

Answer 12

(x1,y1) is your first point
(x2,y2) is the second

Answer 13

In this case

(x1,y1) = (-2,6)
(x2,y2) = (0,-4)

Answer 14

So it would look like -4-6 over 0-2?

Answer 15

very close, but it should be

-4-6 over 0 - (-2)

Answer 16

So the slope would be -5/1 ?

Answer 17

which reduces to -5

Answer 18

the slope is m = -5

the y-intercept is b = -4 ... this is because f(0) = -4

Answer 19

plug m = -5 and b = -4 into y = mx + b to get

y = mx + b

y = -5x + (-4)

y = -5x - 4

Answer 20

Therefore, the linear function is f(x) = -5x - 4

Answer 21

Awesome. I think I get it now.

Answer 22

That's great that you do