Answer:
f(x) = 3x -5
Explanation:
Pre-Solving
We are given a function.
We want to find the equation of this function.
- We know it is linear.
- We also know that if x = 1, f(x) = -2 and if x = 4, f(x) = 7 (that is what f(1) = -2 and f(4) = 7) mean.
We will write the equation of this function in slope-intercept form (even though there are other ways to write it). Slope-intercept form is given as f(x) = mx+b, where m is the slope and b is the value of y at the y-intercept.
Solving
We first should put our values into points.
f(1) = -2 is (1, -2) and f(4) = 7 is (4, 7).
Now, we need to find the slope of the line.
The slope (m) can be found using
, where
and
are points.
Before we calculate m, let's label the values of the points to avoid any possible confusion.

Now substitute:


Simplify.


m = 3
The slope of the function is 3.
Here's our function so far:
f(x) = 3x + b
We now need to find b.
As the points (1, -2) and (4, 7) pass through the function, we can use their values to help solve for b.
We can take either one, but let's take (1, -2).
Substitute 1 as x and -2 as f(x).
-2 = 3(1) + b
Multiply.
-2 = 3 + b
Subtract.
-5 = b
Substitute -5 as b into the function.
f(x) = 3x - 5