Lesson 5: Slope

​The slope of a line is the change in the y values over the change in the x values. In other words, the slope of a line is how much the line rises or falls over how much the line moves to the right. Usually, we measure this using known points on a line using the formula to the right. In linear equation forms, it is usually represented by m.

Slopes will usually appear as fractions and must always be simplified!​

​There are four types of slopes:

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​Negative slopes move down when read from left to right

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​Positive slopes move up when read from left to right

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​Undefined slopes are vertical (straight up and down) lines

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​Zero slopes are horizontal (straight left-to-right) lines

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​​In linear equations...

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if the value of m is negative, then the line should have a negative slope.

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​if the value of m is positive, then the line should have a positive slope.

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if the statement says x = n (where n is any numerical value), then the slope is undefined.

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if the statement says y = n (where n is any numerical value), then the slope is zero.

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​Given the following points, find whether the lines have a positive slope, negative slope, undefined slope, or zero slope:

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• ​(9, 2) and (2, -3)

• ​(-1, 0) and (3, 2)

• ​(8, 4) and (-5, -4)

​Two lines are parallel to each other if they have the same slopes.

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​Two lines are perpendicular to each other if their slopes are opposite reciprocals. In order for slopes to be opposite reciprocals, they must be opposite signs (one positive and one negative) and flipped fractions of each other (2/3 is the reciprocal of 3/2).