Answer:
The coordinates are given below as
[tex]\begin{gathered} \left(1,2\right)\Rightarrow\left(x_1,y_1\right) \\ \left(5,10\right)\Rightarrow\left(x_2,y_2\right) \end{gathered}[/tex]Concept:
To calcute the equation of a line, we will use the formula below
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]By substituting the values, we will have
[tex]\begin{gathered} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y-y_{1}}{x-x_{1}} \\ \frac{10-2}{5-1}=\frac{y-2}{x-1} \end{gathered}[/tex]Cross multiply the equation above, we will have
[tex]\begin{gathered} \frac{10-2}{5-1}=\frac{y-2}{x-1} \\ \frac{8}{4}=\frac{y-2}{x-1} \\ \frac{2}{1}=\frac{y-2}{x-1} \\ y-2=2\left(x-1\right) \\ y-2=2x-2 \\ y=2x-2+2 \\ y=2x \end{gathered}[/tex]Hence,
The equation of the line is y=2x
