Unit 5

Linear Functions & Their Graphs

Coordinate plane, graphing, slope, slope-intercept, writing equations of lines

In this unit you'll turn equations into pictures, and learn to read a line the way you read a map: where it starts, which way it leans, and how steep it climbs. Picturing the algebra makes a lot of what's ahead easier to follow.

It helps to have a few things fresh first: working with negative numbers, and dropping a number into an expression to see what comes out. A little comfort with rates, like "miles per hour," will feel familiar too. If any of that is rusty, a quick warm-up first will smooth the road.

This is where a function becomes a picture you can read. The one idea threading through every lesson: a line is a linear function. The y = mx + b you'll meet and the f(x) = mx + b from Unit 4 are the same thing under two names. It's that same function machine, now drawn as a straight line.

Here's the reassuring part up front. Slope, the main idea of this unit, isn't new. It's the rate of change, which is the unit rate you met in Unit 3: "how much y changes for each 1 step in x." So when slope shows up, you're meeting something you already know under a new name.

Before each new lesson, redo two or three problems from a lesson or two back from memory first. That small warm-up keeps the earlier moves sharp. In this unit the earlier moves are substituting and signed arithmetic, and those are exactly what trips people up if they've gone rusty.