EN
BuilderGrade 8⏱ 15 min

Slope

Drag two points and measure how steep the line is: rise over run, and y = mx + b.

Standards: 8.EE.B.58.EE.B.68.F.B.4

1Wonder

A road sign says “10% grade”. A wheelchair ramp must not be steeper than 1 in 12. How can a single number describe how steep something is?

2Explore

Slope explorer

This activity needs a bigger screen

Turn your phone sideways, or open this lesson on a tablet or computer. The explanation and quiz below work here.

-6-4-2246-4-224run = 5rise = 3(-2, -1)(3, 2)m = rise / run= 3 / 5 = 3/5 ≈ 0.6y = (3/5)x + 0.2Uphill: positive slopeSillyChili
👆 Drag the two points
Try this
  • Drag the points so the line goes downhill. What is the sign of the slope?
  • Make the line flat. Now make it straight up. What happens to the slope?
  • Find two different pairs of points on the same line. Is the slope the same?
  • Make a line with slope 2, then one with slope 1/2. Which is steeper?

3Explain

SillyChili
Step 1 of 5

Slope measures steepness

Both ramps go up, but one is much steeper. Slope is a number that tells exactly how steep a line is.

Slope between two pointsm=y2−y1x2−x1=riserunm = \frac{\htmlClass{c-red}{y_2 - y_1}}{\htmlClass{c-blue}{x_2 - x_1}} = \frac{\htmlClass{c-red}{\text{rise}}}{\htmlClass{c-blue}{\text{run}}}

Example. Through (1,2)(1, 2) and (4,8)(4, 8): m=8−24−1=63=2m = \dfrac{8 - 2}{4 - 1} = \dfrac{6}{3} = 2. Then b=2−2⋅1=0b = 2 - 2 \cdot 1 = 0, so the line is y=2xy = 2x.

4Practice

Question 1 of 5

What is the slope of this line?

5Recap

  • Slope tells how steep a line is: m=riserunm = \dfrac{\text{rise}}{\text{run}}.
  • Any two points on a line give the same slope.
  • Uphill → positive, downhill → negative, flat → 0, vertical → undefined.
  • In y = mx + b, m is the slope and b is the y-intercept.
  • Bigger |m| means steeper.