iitwe are asked to determine the equation of the given line in the graph. To do that we will use two points through which the line passes.
[tex]\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(3,2) \end{gathered}[/tex]Now we will find the slope of the line using the following equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the values:
[tex]m=\frac{2-1}{3-0}=\frac{1}{3}[/tex]Now we use the general form of a line equation:
[tex]y=mx+b[/tex]Replacing the value of "m":
[tex]y=\frac{1}{3}x+b[/tex]Now, to find the value of "b" we replace the first point, that is (x, y) = (0, 1):
[tex]\begin{gathered} 1=\frac{1}{3}(0)+b \\ 1=b \end{gathered}[/tex]replacing the value of "b":
[tex]y=\frac{1}{3}x+1[/tex]And thus we get the equation of the line.
