Given the points (5,2) and (10,4), we can find the slope of the line that passes through them with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]in this case we have the following:
[tex]\begin{gathered} (x_1,y_1)=(5,2) \\ (x_2,y_2)=(10,4) \\ \Rightarrow m=\frac{4-2}{10-5}=\frac{2}{5} \\ m=\frac{2}{5} \end{gathered}[/tex]now that we have that the slope is m = 2/5, we can find the equation of the line using the first point and the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-2=\frac{2}{5}(x-5)=\frac{2}{5}x-5\cdot(\frac{2}{5})=\frac{2}{5}x-2 \\ \Rightarrow y=\frac{2}{5}x-2+2=\frac{2}{5}x \\ y=\frac{2}{5}x \end{gathered}[/tex]therefore, the equation of the line that contains the points (5,2) and (10,4) is y = 2/5 x
