The slope m of a line can be obtained by the formula:
[tex]m=\frac{\Delta y}{\Delta x}[/tex]where Δy is the difference between the y-coordinates of two points on the line and Δx is the difference between the respective x-coordinates of those points.
So, we need to use two points on the line to find the slope. The first one we are told to use is the y-intercept, i.e., the point where the line crosses the vertical axis: (0, 50).
The other point we are told to use is the purple dot, i.e., (30, -40).
Notice that the first entry of each point corresponds to its x-coordinate, and the second entry corresponds to its y-coordinate. Thus:
[tex]m=\frac{-40-50}{30-0}=-\frac{90}{30}=-\frac{9}{3}=-3[/tex]Therefore, the slope is -3.