Equation of a line in slope-intercept form
y = mx + b
where m is the slope and b is the y-intercept
From the graph, we can see that the line intercepts the y-axis at the point (0,-3), then b = -3.
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, the line passes through the points (0, -3) and (2, -2), then its slope is:
[tex]m=\frac{-2-(-3)}{2-0}=\frac{-2+3}{2}=\frac{1}{2}[/tex]
Substituting with m = 1/2 and b = -3 into the equation, we get:
[tex]\begin{gathered} y=\frac{1}{2}x+(-3) \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]
