SOLUTION: 3. Take a look at the table below and write out an equation for f(x). x -2 -1 0 1 2 f(x) -2 2 6 10 14 each of these items (x, -2, -1, 0, 1, 2) are suppose to be in a block in

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 3. Take a look at the table below and write out an equation for f(x). x -2 -1 0 1 2 f(x) -2 2 6 10 14 each of these items (x, -2, -1, 0, 1, 2) are suppose to be in a block in      Log On


   

Question 198059: 3. Take a look at the table below and write out an equation for f(x).
x -2 -1 0 1 2
f(x) -2 2 6 10 14
each of these items (x, -2, -1, 0, 1, 2) are suppose to be in a block in the first row of the table and (f(x) , -2, 2, 6, 10, 14 are on the next row of the table. The table just didn't copy over when I cut and pasted.
I am so lost in this algebra class, I don't even know where to begin with this, little alone find an answer. Please answer. Thank you
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Notice how when x increases by 1, f(x) increases by 4 (eg as x goes from 0 to 1, f(x) goes from 6 to 10)


Since this increase is the same for any x value, this means that f(x) is a linear function.


So to find the equation, all we need are two points.


So let's find the equation through the points (0,6) and (1,10)


First let's find the slope of the line through the points and


Note: is the first point and is the second point .


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%2810-6%29%2F%281-0%29 Plug in y%5B2%5D=10, y%5B1%5D=6, x%5B2%5D=1, and x%5B1%5D=0


m=%284%29%2F%281-0%29 Subtract 6 from 10 to get 4


m=%284%29%2F%281%29 Subtract 0 from 1 to get 1


m=4 Reduce


So the slope of the line that goes through the points and is m=4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-6=4%28x-0%29 Plug in m=4, x%5B1%5D=0, and y%5B1%5D=6


y-6=4x%2B4%28-0%29 Distribute


y-6=4x%2B0 Multiply


y=4x%2B0%2B6 Add 6 to both sides.


y=4x%2B6 Combine like terms.


So the equation that goes through the points and is y=4x%2B6


This means that the function is f%28x%29=4x%2B6


Now if we pick a random x value that we haven't used yet, say x=2, and plug it in, we get:

f%282%29+=+4%282%29%2B6=8%2B6=14


So when x=2, f%28x%29=14 which supports our answer (try other x values to confirm).

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If you plot the points on a graph, is and is , then you can see that they lie in a straight line.



So we are looking for a function that looks like:



One of the points is (0, 6), so we can determine the value of directly, since 6 is clearly the y-intercept. So far we have:



Now we need the value of

Pick any two pairs of values (let's use (0, 6) and (1, 10)) and plug them into:





Now we have:



Finally, you need to check the work. For each pair of numbers in your table, substitute the value and the value into the derived function. It must result in a true statement in each case.



checks.

Now, you do the rest.


John