Find the slope of the line that goes through the points (-4, 4) and (4, 6).

Question

Find the slope of the line that goes through the points (-4, 4) and (4, 6). I get really confused so could you please show the steps?

Answer 1

There are several ways of considering this. First, I'll discuss the "Formula" method. Slope (aka "m") is calculated using:

Where two points on the line are (x₁, y₁) and (x₂, y₂). In this case the points are (-4, 4) and (4, 6). You get to select which point you want to be (x₁, y₁); let's select (-4, 4). That means x₁ = -4 and y₁ = 4. That makes (x₂, y₂) the point (4, 6) or x₂ = 4 and y₂ = 6. So just plug in the points:

m = (6 - 4)/(4 - -4)

m = (6 - 4)/(4 + 4)

m = 2/8

m = 1/4

Another way to think about it is to use the "Slope Triangle" method:

The slope is the change in "y" divided by the change in "x". As you can see, y canges by 2 and x changes by 8 so m = 2/8 = 1/4

Answer 2

Given two points and a line that is linear, we simply need to calculate our rise over run between the two points.

Let's say that point A is (-4,4) and point B is (4, 6). I am only giving them names to make the explanation easier.

Our rise correlates to our change in y between the two points, which would be the difference between the two y-values. So, the y-value for point B is 6, and the y-value for point A is 4. The difference between the two would be 6-4 = 2.

Our run correlates to our change in x between the two points. Our x-value for B is 4, and our x-value for A is -4. The difference between the two would be 4-(-4) = 8.

Now we just have to put them together to find our slope (rise/run). This gives us 2/8 which simplifies to 1/4 or 0.25. So our slope is one fourth.