To solve the exercise, we can first find the slope of the line that passes through the given points using the following formula:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through the line passes} \end{gathered}[/tex]
So, in this case, we have:
[tex]\begin{gathered} (x_1,y_1)=(1,2) \\ (x_2,y_2)=(2,5) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{5-2}{2-1} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]
Now, we can use the point-slope formula to find the equation of the line in its slope-intercept form:
[tex]\begin{gathered} y-y_1=m(x-x_1)\Rightarrow\text{ Point-slope formula} \\ y-2=3(x-1) \\ \text{ Apply the distributive property to the left side of the equation} \\ y-2=3\cdot x-3\cdot1 \\ y-2=3x-3 \\ \text{ Add 2 from both sides of the equation} \\ y-2+2=3x-3+2 \\ y=3x-1 \end{gathered}[/tex]
Therefore, the equation that represents the line that passes through the given points is
[tex]$\boldsymbol{y=3x-1}$[/tex]
