Find the slope of the line shown.
Slope is equal to the vertical change divided by the horizontal change. And when looking at these changes, we need to go left to right. For a vertical change, up is positive and down is negative. And for horizontal change, right is positive and left is negative. So let’s go ahead and pick two points on this line.
Here, we are at the point negative five, one and here, we are at the point negative one, negative four. So moving left to right, let’s look at the vertical change. We need to go down: one, two, three, four, five. So our slope is negative five divided by something — our horizontal change. So from here, we need to go right: one, two, three, four. And that will be positive four since we went to the right. And this does not reduce. So our slope will be negative five-fourths.
Now we also could have solved this using the slope formula. And the slope formula 𝑚 represents the slope. And it is equal to 𝑦 two minus 𝑦 one divided by 𝑥 two minus 𝑥 one. So negative five, one was the first point that we looked at. That would be 𝑥 one, 𝑦 one. And then, negative one, negative four will be 𝑥 two, 𝑦 two — our second point.
So let’s go ahead and plug these in. 𝑦 two minus 𝑦 one would be negative four minus one. And then 𝑥 two minus 𝑥 one would be negative one minus negative five. So for our numerator, negative four minus one is negative five. And on the denominator, two negatives make a positive. So negative one plus five is positive four. So once again, our final answer is negative five-fourths. This is our slope of this line.