Math 1 · Unit 3 · Lesson 1 · part 4 of 6

From a table, from two points, and reading the number

Each step of x is 1, and each time y goes up 3.

From a table, from two points, and reading the number

From a table

x	0	1	2	3
y	5	8	11	14

Each step of x is 1, and each time y goes up 3. Rise 3, run 1. Slope = 3.

If the x steps are bigger, divide: x goes 0, 2, 4 and y goes 5, 11, 17. Rise 6 over run 2: slope = 62 = 3. Same line.

From two points

Points (2, 3) and (6, 11). Rise: subtract the y values, second minus first: 11 − 3 = 8. Run: subtract the x values in the same order: 6 − 2 = 4.

Slope = 84 = 2.

Points (1, 7) and (4, 1): rise 1 − 7 = −6, run 4 − 1 = 3. Slope = −63 = −2. Falling.

Same order on top and bottom, always, or the sign comes out wrong.

Positive slopeRise up, so the line climbs left to right. y = 2x has slope 2.

Negative slopeRise down, so the line falls left to right. Slope −12 falls gently.

Zero slopeRise 0: y never changes. A flat horizontal line, like y = 4. Slope 0.

No slopeA straight up-and-down vertical line, like x = 3. Run 0, and you cannot divide by 0. We say the slope is undefined.

The vertical line at x = 4 is drawn too. Between any two of its points the run is 0, so the fraction has a 0 on the bottom, and there is no such number. That is the one line with no slope.

Where to go next

Next: Count it yourselfThree lines on grids. All the partsSlope: The Rate of Change Gets Its Name