Let us take two points from the table values,
(5,4) and (10,7)
To find the equation:
First, find the slope of th equation
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{7-4}{10-5} \\ =\frac{3}{5} \end{gathered}[/tex]
Then, substitute the slope in the slope intercept form of an equation,
[tex]\begin{gathered} y=mx+c \\ y=\frac{3}{5}x+c\ldots\ldots.(1) \end{gathered}[/tex]
Next, lets find the y-intercept c:
Since, the equation passes through the point (5,4) ,
Hence,
[tex]\begin{gathered} 4=\frac{3}{5}(5)+c \\ 4=3+c \\ c=1 \end{gathered}[/tex]
Substitute c=1 in equation (1) we get,
[tex]y=\frac{3}{5}x+1[/tex]
Hence, the correct option is C.
