Respuesta :

joshlind3

Answer:

[tex]y = 2x + 3[/tex]

Step-by-step explanation:

First, we can find the slope of the line.

[tex]m = \frac{y1-y2}{x1-x2}\\m=\frac{9-5}{3-1}\\m = \frac{4}{2}=2\\[/tex]

Using the [tex]y = mx + b[/tex] equation, we can solve for b

[tex]9 = 2(3)+b\\9 = 6 + b\\b = 9-6 = 3[/tex]

Let's see if [tex]y = 2x + 3[/tex] works

[tex]2(1) + 3 \\2 + 3 = 5\\\\2(3) + 3\\6 + 3 = 9[/tex]

It checks out!

weakster
If f(1)=5 and f(3)=9 we are given two points, so we can use the slope intercept form to find the equation of f(x)

Points:(1,5),(3,9)

Slope intercept form: y2-y1=m(x2-x1)

9-5=m(3-1)
4=m(2)
m=2

f(x)=2x+b Plug in a point and solve for b

5=2(1)+b
3=b

Answer: f(x)=2x+3

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