Step 1
State the equation of line that can be used to model the values on the table.
[tex]y-y_1=\text{ }\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Where
[tex]\begin{gathered} y_1=\text{ 8} \\ y_2=\text{ 12} \\ x_1=2 \\ x_2=4 \end{gathered}[/tex]
Step 2
Put in the value and find the equation of the line.
[tex]\begin{gathered} y-8=\frac{12-8}{4-2}(x-2) \\ y-8=\frac{4}{2}(x-2) \\ y-8=2x-2(2) \\ y=2x-4+8 \\ y=2x+4 \\ \end{gathered}[/tex]
Step 3
Given an output of 120feet, find the input
[tex]\begin{gathered} 120\text{ = 2}x+4 \\ 120-4=2x \\ 2x=116 \\ \frac{2x}{2}=\frac{116}{2} \\ x=58\text{ seconds} \end{gathered}[/tex]
Hence, the input is 58seconds.
