Question

If f(x) is a linear function, f(-2) = -5, and f(5) = -4, find an equation for f(x)

Answer 1

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Answer 2

Well, "linear function" just means that it's an equation for a line. So you can use any line form that you like: y=mx+b or \(y-y_1=m(x-x_1)\).

Either way, you need the slope and a point. You are given f(-2) = -5, and f(5) = -4... well, those are just 2 points on the line, right?

Remember, this is just function notation. y=f(x).

So you are given that y=-5 when x=-2. That means that the point (-2,-5) is one point on the line.

Get the other point from f(5) = -4.

Now you have two points, so you can find slope, then use the slope and either point to find the equation for the line.