To find the equation of the line shown, we need two points:
[tex]\begin{gathered} (x_1,y_1)=(0,100) \\ \text{and} \\ (x_2,y_2)=(20,200) \end{gathered}[/tex]
The equation of the line goes by:
[tex]y-y_1=m(x-x_1)[/tex]
The find m, the slope, we use the formula below and find m.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}_{} \\ m=\frac{200-100}{20-0} \\ m=\frac{100}{20} \\ m=5 \end{gathered}[/tex]
Now, let's put the point and m to find the equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-100=5(x-0) \\ y-100=5(x) \\ y-100=5x \\ y=5x+100 \end{gathered}[/tex]
Changing to functional notation, this will be:
[tex]f(x)=5x+100[/tex]
2nd answer choice is correct.
