Question

Write a linear function that satisfies the given conditions? f(0) = 7/2, f(9) = 5/2

Answer 1

`y = -1/9x + 7/2`

Explanation:

We need to find the pieces for `y = mx + b`

`f(0) = 7/2` or `(0 , 7/2)` or `(0, 3.5)`

`f(9) = 5/2` or `(9, 5/2)` or `(9 , 2.5)`

Now let's use this formula to find the slope:

`m = ( y_2 - y_1 )/( x_2 - x_1 )`

`m = ( 7/2 - 5/2 )/( 0 - 9 )`

`m = - (2/2)/9`

`m = -1/9`

We have the slope for `y = mx + b` but we still need that `b` (the `y`-intercept)

To find that, we need to find the value of `y` when `x = 0`

HEY! That's what's going on in `f(0) = 7/2`

So now we have `b = 7/2`, `m = -1/9`

Let's make our equation:

`y = -1/9x + 7/2`

Let's graph our formula and make sure it passes through these points

graph{y = -1/9x + 7/2}

Yep, it passes through these points, nice work!