Given the table below
To find the equation of the values of the table, we will first calculate the rate of change, then use a point and the rate of change calculated fo find the equation for the repairman's charges for the repair
To find the rate of change we have
[tex]\text{ Point 1}\Rightarrow(1,62)\Rightarrow t_1=1,c_1=62[/tex][tex]\text{ Point 2}\Rightarrow(3,116)\Rightarrow t_2=3,c_2=116[/tex]
The rate of change formula is
[tex]m=\frac{c_2-c_1}{t_2-t_1}=\frac{116-62}{3-1}=\frac{54}{2}=27[/tex]
Having calculated the rate, we can use slope and one point form equation of a line to get the desired equation. This is given below:
[tex]c-c_1=m(t-t_1)[/tex]
Substitute the given values of t and c and the rate in the formula above
[tex]\begin{gathered} c-62=27(t-1) \\ c-62=27t-27 \\ c=27t-27+62 \\ c=27t+35 \end{gathered}[/tex]
Hence, the repairman's charges for a repair is given as C = 27t + 35
