If a linear function f satisfies the given conditions, find f(x); f(- 2) = 6 and f(4) = - 3 . Hint: Remember that y = f(x) If f(7) = 5 , then (7, 5) is an ordered pair on the graph of the linear

Question

If a linear function f satisfies the given conditions, find f(x); f(- 2) = 6 and f(4) = - 3 . Hint: Remember that y = f(x) If f(7) = 5 , then (7, 5) is an ordered pair on the graph of the linear function f. f(x)=

Answer 1

1. We're given a linear function and here are the things we know about it: we know that f(-2) = 6, and that f(4) = -3. To shorten things, let's list these values as (-2,6) and 4(-3).
2. What we NEED to know for this function, is the slope, m, and the y-intercept.
3. All linear functions follow the same procedure we want to know more about their graphs:

1. f(x) = mx+b, and...

Y₂ - Y₁

m = _____________

X₂ - X₁

1. Let's solve for the slope first. Remember, our paired values are (-2,6) and (4,-3)

m = -3 - 6______ = -9 = -3 (You can simplify this fraction if you'd like)

4 - (-2) 6 2

1. So our slope, m, for this function is -3/2 .
2. Now, we need to find the y-intercept, the b value. Since we have the slope, we can just plug that in one of the ordered pairs we made for the function earlier. I'm going to use (-2,6) to solve for b.

6 = -3 ( -2) + b => 6 = 3 + b => 3 = b

2 -3 -3

1. We have our y-intercept, along with our slope. So let's create a function for this problem:

f(x) = -3x + 3

2

This is your answer for the problem!