Let f be a linear function such that f(1) = 5 and f(3) = 9. Find an equation for f(x).

Step-by-step explanation:

So we know that:

In other words, we have 2 coordinates: (1,5) and (3,9).

With this, we can figure out the slope. Let (1,5) be x₁ and y₁ and let (3,9) be x₂ and y₂. The slope formula is:

Substitute:

So, the slope is 2.

Now, use the point-slope form to figure out the y-intercept. The point-slope form is:

For consistency, let's continue to use (1,5) as x₁ and y₁. Now, we can use 2 as m. Thus:

Distribute:

Add 5 to both sides:

So:

And that's our equation :)

ddd

step-by-step explanation: