Answer :
The slope-intercept form is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept (value y at x = 0)
Since y represents the amount of money he saves and x represents the number of weeks, then
x = 2 and y = 180
x = 4 and y = 260
We will use them to find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Substitute y2 by 260 and y1 by 180, x2 by 4, and x1 by 2
[tex]\begin{gathered} m=\frac{260-180}{4-2} \\ m=\frac{80}{2} \\ m=40 \end{gathered}[/tex]The equation is
[tex]y=40x+b[/tex]To find b substitute x by 2 and y by 180
[tex]\begin{gathered} 180=40(2)+b \\ 180=80+b \end{gathered}[/tex]Subtract 80 from both sides
[tex]\begin{gathered} 180-80=80-80+b \\ 100=b \end{gathered}[/tex]The equation is
[tex]y=40x+100[/tex]