What is the rate of change(slope)

Let’s use the slope formula to calculate the slope of a line, using just the coordinates of two points. The line passes through the points (1, 4) and (-1, 8). Let’s call the point (1, 4) point 1, and the point (-1, 8) point 2. That means x1 = 1, y1 = 4, x2 = -1, and y2 = 8.

Example

Points

Coordinates

(1, 4)

x1 = 1

y1 = 4

(-1, 8)

x2 = -1

y2 = 8

The slope formula is . When we put the coordinates into the formula, we get the equation . This reduces to m = -2. The slope of the line is -2.

It is important to realize that it doesn’t matter which point is designated as 1 and which is 2. We could have called (-1, 8) point 1, and (1, 4) point 2. In that case, putting the coordinates into the slope formula produces the equation . Once again, that simplifies to m = -2. That’s the same slope as before.

Step-by-step explanation:

Slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run: . This simple equation is called the slope formula.

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step-by-step explanation:

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