Here is a line with a few of the points labeled.

We can use what we know about slope to decide if a point lies on a line.

First, use points and slope triangles to write an equation for the line.

• The slope triangle with vertices $(0,1)$ and $(2,5)$ gives a slope of $\frac{5-1}{2-0} =2$.
• The slope triangle with vertices $(0,1)$ and $(x,y)$ gives a slope of $\frac{y-1}{x}$.
• Since these slopes are the same, $\frac{y-1}{x} = 2$ is an equation for the line.

To check whether or not the point $(11,23)$ lies on this line, we can check that $\frac{23-1}{11} =2$. Since $(11,23)$ is a solution to the equation, it's on the line!