# How do you find the slope of (4,5) and (9,-10)?

Feb 3, 2015

Slope is defined as the difference in $y$ per unit $x$

As we don't have units here, we divide the change in $y$ by the change in $x$, or in formula ($\Delta$ means change):
Slope= $\frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 10 - 5}{9 - 4} = \frac{- 15}{5} = - 3$

Now we're at it we can also define the whole equation:

Just put in the numbers for one of the points:
$y = a x + b \to 5 = - 3 \cdot 4 + b \to b = 17$
So the equation will be: $y = - 3 x + 17$
graph{-3x+17 [-44.86, 59.17, -26.06, 25.96]}
$- 3 x + 17 = - 3 \cdot 9 + 17 = - 10$ which is correct.