Graph proportional relationships; slope as unit rate · lesson

Slope is the unit rate

💡 For a line through (0, 0), the slope is y ÷ x for any point on it, and it equals the unit rate.

Slope tells how much y goes up when x goes up by 1. For a proportional line, that is the unit rate.

If the line goes through (0, 0) and a point (x, y), the slope is y ÷ x.

The point (1, r) is on every proportional line, where r is the unit rate.

🧠 Let's work it out

A line goes through (0, 0) and (5, 17.5). Find the slope.

What do you think comes next?

💡 Find the slope, then multiply to get y or divide to get x.

A proportional line has the rule y = mx, where m is the slope.

To find y for a new x, multiply x by the slope. To find x for a new y, divide y by the slope.

🧠 Let's work it out

A proportional line goes through (4, 10). What x goes with y = 35?

What do you think comes next?

💡 Write both relationships as a slope; the bigger slope is the steeper line and the faster rate.

One rule might be an equation. Another might be a graph or a price. Turn each one into a slope.

The bigger slope means a steeper line and a faster rate. To see how far apart they get, use both rules at the same x.

🧠 Let's work it out

Rule A is y = 2x. Line B goes through (0, 0) and (3, 7.5). At x = 6, how much more does B give than A?

What do you think comes next?