SOLUTION: Suppose that g(x)is a linear function and also that g(1)=12 and g(-2)=-3. Find an algebraic formula for g(x). I am so lost here. I am probably reading way to far into this que

Algebra ->  Linear-equations -> SOLUTION: Suppose that g(x)is a linear function and also that g(1)=12 and g(-2)=-3. Find an algebraic formula for g(x). I am so lost here. I am probably reading way to far into this que      Log On


   

Question 318082: Suppose that g(x)is a linear function and also that g(1)=12 and g(-2)=-3. Find an algebraic formula for g(x).

I am so lost here. I am probably reading way to far into this question but I have no idea where to start. Any help would be greatly appreciated.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since g(1)=12 and g(-2)=-3, this means that the points (1,12) and (-2,-3) lie on the line. So all we need to do is find the equation of the line that goes through (1,12) and (-2,-3).


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


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=12.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=-3.


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


m=%28-3-12%29%2F%28-2-1%29 Plug in y%5B2%5D=-3, y%5B1%5D=12, x%5B2%5D=-2, and x%5B1%5D=1


m=%28-15%29%2F%28-2-1%29 Subtract 12 from -3 to get -15


m=%28-15%29%2F%28-3%29 Subtract 1 from -2 to get -3


m=5 Reduce


So the slope of the line that goes through the points and is m=5


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-12=5%28x-1%29 Plug in m=5, x%5B1%5D=1, and y%5B1%5D=12


y-12=5x%2B5%28-1%29 Distribute


y-12=5x-5 Multiply


y=5x-5%2B12 Add 12 to both sides.


y=5x%2B7 Combine like terms.


So the equation that goes through the points and is y=5x%2B7


Now simply replace 'y' with g(x) to get g%28x%29=5x%2B7


So the linear function is g%28x%29=5x%2B7