Points are important parts of a line. It takes at least two points to define a line. You have already seen how two point determine where a line is located. But there is another very important quality:  the slope of the line. The slop is like the "slant" or "steepness" of a line on the coordinate plane.

• A line with a positive slope rises from left to right.
• A line with a negative slope falls from left to right.
• A line with zero slop is a horizontal line.
• A line with an infinite (undefined) slope is a vertical line.

Example

For a certain line plotted on a coordinate plane, the slope increases upward four units in the y direction for every three in the positive-x direction. What is the slope of the line.

Procedure

The change in y is +4 and the change in x is +3

The equation to solve is:
Substituing the known values:  slope = 4/3 = 1.5

So the slope of the line is 1.5.

Given Two Points, Find the Slope of the Line

Show the graph

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Examples & Exercises

You don't need a graph to find the slope of a line. All you need is the coordinates of two points.

Example

Suppose you are given these coordinates for two points on a coordinate plane: (4, 10) and (2, 4).

Step 1:  Assign the points.

Remember, it makes no difference which point you consider (x₁,y₁) and (x₂, y₂), just as long as you are consistent. So let's let (4,10) be point 1,  and (1,4) be point 1.

Step 2: Set up the equation and plug in the numerical values.

Step 3: Complete the math.

The slope is positive, so the line rises from left to right. The slope is 2, so the line rises 2 units upward for each unit to the right.

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Examples & Exercises

x1 = 5

y1 = 3

x2 = -5

y2 = -3

m = -3 - 3/5 - 5