Answer:
[tex]f(x)=2x+3[/tex]
Step-by-step explanation:
So we know that:
[tex]f(1)=5 \text{ and } f(3)=9[/tex]
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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\frac{9-5}{3-1}\\m=4/2=2[/tex]
So, the slope is 2.
Now, use the point-slope form to figure out the y-intercept. The point-slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
For consistency, let's continue to use (1,5) as x₁ and y₁. Now, we can use 2 as m. Thus:
[tex]y-(5)=2(x-1)[/tex]
Distribute:
[tex]y-5=2x-2[/tex]
Add 5 to both sides:
[tex]y=2x+3[/tex]
So:
[tex]f(x)=2x+3[/tex]
And that's our equation :)
