# 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 ->  -> 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

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 Click here to see ALL problems on Linear-equations 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(29613)   (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 and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 12 to both sides. Combine like terms. So the equation that goes through the points and is Now simply replace 'y' with g(x) to get So the linear function is