Question

5. The table shows the amount of money, A, in a savings account after mmonths. Select ALL the equations that represent the relationship betweenthe amount of money, A, and the number of months, m.*number ofmonthsdollaramount51,20061,30071,40081,500

Answer 1

`\begin{gathered} \text{Solve for slope }m \\ m=(y-y_0)/(x-x_0) \\ \text{choose any two points in the table, for this one, we choose} \\ (5,1200)\text{ and }(6,1300) \\ m=(1300-1200)/(6-5) \\ m=(100)/(1)=100 \\ \text{The equation can be thought of in a slope intercept form} \\ y=mx+b \\ \text{Solve for }b \\ y=mx+b,\text{ use any of the two points, for this one, we use }(5,1200) \\ 1200=(100)(5)+b \\ 1200=500+b \\ 1200-500=b \\ 700=b \\ \text{Substitute the }m\text{ and }b \\ y=100x+700 \\ \text{change }y\text{ to }A,\text{ and }x\text{ to }m \\ A=100m+700,\text{ rearranging we can also get} \\ A-700=100m\text{ (answer)} \\ A=700+100m\text{ (answer)} \\ A=1200+100(m-5)\text{ (answer)} \end{gathered}`