Use the graph below to find the slope.

We need an accurate way to count the rise and run of the line. We don't have to use any fancy equipment, just a few good points.

Looking at the graph, (-1, 3) and (0, -1) are both on the line. Let's go with those. Now, to go from our first point, (-1, 3), to our second point, (0, -1), we need to go down 4 units and right 1 unit. Moving downward counts as a negative rise, of -4.

Our slope is -4.

Find the slope of the line passing through (0, -0.5) and (1, -3.5).

Our formula for the slope is .

It doesn't matter which point is (x₁, y₁) and which is (x₂, y₂), so let's do whatever we want with them. We'll have (x₁, y₁) = (0, -0.5) and (x₂, y₂) = (1, -3.5).

The slope of this line is -3.

Find the slope between the points (1, 3) and (1, 4).

When all we have is a formula for the slope, everything starts to look like points for plugging in. It works this time, but who knows whom we might hurt in the future with our reckless mathematics?

Nope, not gonna do it. We are not dividing by 0. That makes our slope undefined.

Are the lines passing through these points parallel, perpendicular, or neither?

(1, 5) and (-1, 1)

(-1, -9) and (2, -3)

We're plugging, we're chugging, and we're getting the right answer.

There's no stopping us now.

The lines share a slope, so they are parallel.