The equation of the line can be found using the two-point formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]
From the graph, the intercept points are:
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(3,0) \end{gathered}[/tex]
Applying the formula,
[tex]\begin{gathered} \frac{0-(-3)}{3-0}=\frac{y-(-3)}{x-0} \\ \frac{3}{3}=\frac{y+3}{x} \\ 1=\frac{y+3}{x} \\ \text{cross multiply,} \\ y+3=x \\ \text{collect like terms} \\ y=x-3 \end{gathered}[/tex]
Therefore, the equation of the line is y = x + [- 3] or y = x - 3
