Answer:
y = x + 2 is the required answer.
Step-by-step explanation:
From the graph, we see that the points [tex]$ (1, 3) $[/tex] and [tex]$ (2, 4) $[/tex].
When two points on a line are given, say [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] then we use the two - point formula to determine the equation of the line.
Two point formula: [tex]$ \frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1} $[/tex]
Here, [tex]$ (x_1, y_1) = (1, 3) $[/tex] and [tex]$ (x_2, y_2) = (2, 4) $[/tex].
Therefore, the equation of the line will be:
[tex]$ \frac{y - 3}{4 - 3} = \frac{x - 2}{2 - 1} $[/tex]
[tex]$ \implies \frac{y - 3}{1} = \frac{x - 1}{1} $[/tex]
[tex]$ \implies y - 3 = x - 1 $[/tex]
[tex]$ \implies y = x - 1 + 3 $[/tex]
[tex]$ \implies \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{x + 2}[/tex]
Hence, the answer.
