y-7500=m(x-2.28) get s(x)=m x+d

Question

how would you simplify this: y-7500=m(x-2.28) get s(x)=m x+d

Answer 1

The goal is to get the final answer into the form y = mx + b.  The important features of this final equation is that the y variable is all by itself, and the term with the x is listed first on the right hand side.  The constant is left for last.

 

Start with the original equation:

y - 7500 = m(x - 2.28)

 

First, distribute the m

 

y - 7500 = mx - 2.28m

 

To get the y by itself, add 7500 to both sides.

 

y = mx - 2.28m +7500

 

This can be written as 

 

y = mx + (7500 - 2.28m)

 

finally change this to function notation, s(x)

 

s(x) = mx + (7500 - 2.28m)

 

Now all of the parts are in the right position.  Notice that the constant contains the letter m; that is ok.  Though typically the letter m is designated for the slope, it really only means some unknown constant in this problem.  That is why the -2.28m is grouped with the 7500 as one big constant.  

Answer 2

We can rearrange the equation as

y = mx-2.28m+7500

since y is a function of x, y=s(x)

so, s(x) = mx-2.28m+7500

where -2.28m + 7500 represents the constant d