Question

What is the slope? Use the y-intercept and the purple dot. Exact answer required.

Answer 1

The slope m of a line can be obtained by the formula:

`m=(\Delta y)/(\Delta x)`

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:

`m=(-40-50)/(30-0)=-(90)/(30)=-(9)/(3)=-3`

Therefore, the slope is -3.