SOLUTION: Suppose f(x) is a linear function such that f(-1/2) = -7 and f(1) = -3. What is f(-3)? Thank you!

Algebra ->  Functions -> SOLUTION: Suppose f(x) is a linear function such that f(-1/2) = -7 and f(1) = -3. What is f(-3)? Thank you!       Log On


   

Question 1068458: Suppose f(x) is a linear function such that f(-1/2) = -7 and f(1) = -3. What is f(-3)? Thank you!
Found 2 solutions by Edwin McCravy, math_helper:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

That's just a fancy way of asking this question:

What is the equation of the line that passes through the two points 
%28matrix%281%2C3%2C-1%2F2%2C%22%2C%22%2C-7%29%29 and %28matrix%281%2C3%2C1%2C%22%2C%22%2C-3%29%29,
then what is y when x = -3?

First use the slope formula:

m%22%22=%22%22%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m%22%22=%22%22%28%28-3%29-%28-7%29%29%2F%28%281%29-%28-1%2F2%29%29

m%22%22=%22%22%28-3%2B7%29%2F%281%2B1%2F2%29

m%22%22=%22%22%28-3%2B7%29%2F%282%2F2%2B1%2F2%29

m%22%22=%22%224%2F%283%2F2%29

m%22%22=%22%224%22%F7%223%2F2

m%22%22=%22%224%22%22%2A%22%222%2F3

m%22%22=%22%228%2F3

Then substitute in the point-slope formula:

y-y%5B1%5D%22%22=%22%22m%28x-x%5B1%5D%29

y-%28-7%29%22%22=%22%22expr%288%2F3%29%28x-%28-1%2F2%29%5E%22%22%29

y%2B7%22%22=%22%22expr%288%2F3%29%28x%2B1%2F2%29

Multiply both sides through by 3

3y%2B21%22%22=%22%228%28x%2B1%2F2%29

3y%2B21%22%22=%22%228x%2B4

Solve for y

3y%22%22=%22%228x-17

y%22%22=%22%22expr%288%2F3%29x-17%2F3

Finally substitute f(x) for y:

%22f%28x%29%22%22%22=%22%22expr%288%2F3%29x-17%2F3

Then substitute -3 for x:

%22f%28-3%29%22%22%22=%22%22expr%288%2F3%29%28-3%29-17%2F3

%22f%28-3%29%22%22%22=%22%22-8-17%2F3


%22f%28-3%29%22%22%22=%22%22-24%2F3-17%2F3


%22f%28-3%29%22%22%22=%22%22-41%2F3

Edwin

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Linear function means the relation of f(x) to x has x raised to the first power.
Thus, we can write:
f(x) = mx+b
—
f(-1/2) = -7 —> -7 = m*(-1/2) + b (1)
f(1) = -3 —> -3 = m*(1) + b (2)
—
Subtract (2) from (1) to get one equation with just 'm':
-4 = -(3/2)m
m = 8/3
—
Plug 8/3 in for 'm' in (1) (or (2)) and solve for 'b':
-7 = (8/3)(-1/2) +b
b = -17/3
—
Now we have:
+f%28x%29+=+%288%2F3%29x+-+17%2F3+
—
Just plug in x=-3 and you'll have the answer.
I got -41/3.