So the way to calculate the slope from a line on a grid, we know that:
[tex]slope= \frac{rise}{run} [/tex]
If we take the line RC, we count that the number of units that it rises is 3 units. However, it does not go to the right or to the left, therefore, it does not 'run' at all. It will be 0. So when we put this into a fraction:
[tex] \frac{3}{0} [/tex]
we see that this answer comes out undefined. This is because there is a 0 in the denominator - so the slope for RC is undefined.
When we look at the line SC, we see that the units that it rises is -1 units (essentially it went down 1 unit), and we see that the number of units it 'ran' is 5 units. So let's put that into a fraction:
[tex] \frac{-1}{5} [/tex]
and we see that the slope for SC is [tex] \frac{-1}{5} [/tex].
