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

Mar 6, 2018

$y = - \frac{1}{9} x + \frac{7}{2}$

#### Explanation:

We need to find the pieces for $y = m x + b$

$f \left(0\right) = \frac{7}{2}$ or $\left(0 , \frac{7}{2}\right)$ or $\left(0 , 3.5\right)$

$f \left(9\right) = \frac{5}{2}$ or $\left(9 , \frac{5}{2}\right)$ or $\left(9 , 2.5\right)$

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

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{\frac{7}{2} - \frac{5}{2}}{0 - 9}$

$m = - \frac{\frac{2}{2}}{9}$

$m = - \frac{1}{9}$

We have the slope for $y = m x + b$ 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 $f \left(0\right) = \frac{7}{2}$

So now we have $b = \frac{7}{2}$, $m = - \frac{1}{9}$

Let's make our equation:

$y = - \frac{1}{9} x + \frac{7}{2}$

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!