If f ( x ) is a linear function, f ( − 3 ) = − 1 , and f ( 4 ) = 1 , find an equation for f ( x )

Answer 1

Hi there!

In order to find the equation of a line we need some information. IN this case, they are giving us two points. They are just hidden in the f(x) format. The number next to the f is the x coordinate. Remember how f(x) is the same thing as y? So the y coordinate is what it is equal to.

Here are our two points: (-3, -1) (4, 1)

To write an equation in point slope form, y - y₁ = m (x - x₁) we only need the slope!

Do you remember the slope formula? m = y₂ - y₁

x₂ - x₁

Plug in the values we have and simplify. It doesn't matter which point is your first point and which is your second.

( x₁ , y₁) (x₂ , y₂)

(-3, -1) (4, 1)

m = y₂ - y_{1 =} 1 - (-1) = 1 + 1 = 2

x₂ - x₁ 4 - (-3) 4 + 3 7

(Do you know why the minuses turn to pluses here?)

Our slope, m, is 2/7. Let's plug that into the point slope formula.

y - y₁ = m (x - x₁) y - y₁ = (2/7) (x - x₁) Now we just need the point, you can pick either point.

y - 1 = (2/7) (x - 4) or y + 1 = (2/7) (x + 3) And there you have it, an equation!

If you need to write it in slope intercept form, y = mx +b, you just need to solve one of those equations for y.

Let me know if you have any questions! Good luck!

Margaret