Find the slope of the line that passes through (6, 5) and (1, 8). Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answer 1

Hi Jessica,

The slope (typically labeled "m".) of a line is a measure of its "steepness" and is defined as the ratio of rise to run. In other words, (how far up or down)/(how far over).

If we know two points on a line, the rise between them is calculated by subtracting the y-coordinates, while the run is calculated by subtracting the x-coordinates.

Therefore, the slope formula is written as, m = (y₂ - y₁)/(x₂ - x₁).

Where (x₁, y₁) and (x₂, y₂) are two points known to be one the line.

Notice that subscripts (the little "dropped" numbers) don't represent any arithmetic operation, their only purpose is merely to distinguish the coordinates of one point from the other.

Students often ask which is point 1 and which is point 2 or does it even matter.

The answer is it doesn't matter which is which AS LONG AS YOU'RE CONSISTANT!

Personally, I recommend reading the graph from left to right.

That is, I use the left-most point 1 and the point to the right as point 2.

This trick of mine guarantees that my run (the denominator) is always positive.

In this problem the points are (1, 8) and (6, 5)

The left-most point is the one with the smaller x, so point 1 is (1, 8) and point 2 is (6, 5)

This means that x₂ = 6, y₂ = 5, x₁ = 1 and y₁ = 8.

If we plug these numbers into the formula, we get m = (5 - 8)/(6 - 1) = -3/5.

I hope this helps.

Answer 2

Slope = m = change in y / change in x = y₂ - y₁ / x₂ - x₁

(x₁, y₁) = (6, 5)

(x₂, y₂) = (1, 8)

m = y₂ - y₁ / x₂ - x₁ = 8 - 5 / 1 - 6 = 3 / -5

Answer 3

Slope is the change in y over the change in x, sometimes called "rise over run." This looks like the following:

slope = m = (y1-y2)/(x1-x2)

When you plug the coordinates in the equation you have to be consistent with order, it doesn't matter which coordinate you pick first: *(6,5), (1,8)

(5-8)/(6-1) = -3/5

or

(8-5)/(1-6) = 3/-5 = -3/5

Answer 4

slope = -3/5

a line through (6,5) and (1,8) has slope = "rise over run" = difference in y coordinates divided by the corresponding difference in x coordinates: (8-5)/1-6) = 3/-5 = -3/5