Hello!
The slope is [tex] \frac{rise}{run} [/tex]. One way we could do this is find two points on the line and form a right triangle to connect the two. We then divide the rise of this triangle by the run.
We can see the points (-3,-2) and (0,-1). As you can see, our rise is 1, and the run is 3. If we divide our rise by run, we get the slope of 1/3.
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The work we did above can be represented in the following formula.
[tex] \frac{ y_{2} - y_{1} }{ x_{2}- x_{1} } [/tex]
The ones and twos just represent a certain ordered pair. We will have (0,-1) be ([tex] x_{1} , y_{1} [/tex]) and (-3,-2) be ([tex] x_{2} , y_{2} [/tex]). Now we plug our numbers into the formula. Note that the ones and twos can be swapped and the slope will be the same.
[tex] \frac{-2+1}{-3-0} = \frac{-1}{-3} = \frac{1}{3} [/tex]
This proves that our slope is 1/3.
I hope this helps!
