Question

Write a linear function f with the values f(0) = −5 and f(1) =−3.
A function is f(x)=¯

Answer 1

`y=2x-5`

Explanation:

We want to find a linear function
`f(x)` with the values

`f(0)=-5\\f(1)=-3`

These mean that when x is 0, y is -5, and when x is 1, y is -3.

This means that we want to find the equation of a line that goes through the ordered pairs below:

`(0,-5)\\(1,-3)\\`

Let's find the slope between the two ordered pairs. The slope is the rise over the run. The rise is the change in y-values.

`-3--5=-3+5=2`

The change in y-values is 2.

The run is the change in x values.

`1-0=1`

The change in x-values is 1.

The slope is the rise divided by the run, so:

`slope=(2)/(1)=2`

Now that we know the slope, let's find the y-intercept! This is when x equals 0. Luckily, that number is already given! We know that when x equals 0, y equals -5!

`intercept=-5`

Now that we have the slope and intercept, we can plug these numbers into slope-intercept form!

`y=2x-5`