In order to find the line equation, we need to choose 2 points along the line, for instance,
the points
[tex]\begin{gathered} (x_1,y_1)=(0,1)_{} \\ (x_2,y_2)=(1,3)_{} \end{gathered}[/tex]
Then, the slope m of the line will be given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-0}[/tex]
which gives
[tex]m=\frac{2}{1}=2[/tex]
Then, the line has the form
[tex]y=mx+b\Rightarrow y=2x+b[/tex]
We can find the y-intercept denoted by b by substituting one of the two points. For instance, if we substitute point (0,1) into the last result, we get
[tex]\begin{gathered} 1=2(0)+b \\ \text{then} \\ b=1 \end{gathered}[/tex]
Therefore, the line equation in slope-intercept form is given by:
[tex]y=2x+1[/tex]
