Math 1 · Unit 3 · Lesson 3
The Family of Lines: One Form, Many Members
All straight lines share one form, y = mx + b, so they are one family, and each line is a member picked out by its own m and b. Change b and the line slides up or down. Change m and it tilts around its y-intercept. Move the sliders and watch. Then look ahead: every family you meet later gets the same questions.
The big idea
A family of graphs is a group that shares one form and differs only in its numbers. Every straight line is y = mx + b, so all lines are one family, each line is a member, and m and b are the parameters that pick it out. Each parameter has one job: change b and the line slides straight up or down without tilting, which is why lines with the same m are parallel; change m and the line tilts around its y-intercept, steeper for a bigger size, flat at 0, falling when negative. That is the whole habit: name the family, find its numbers, know what each number does. Lines are the first and simplest family, so this is where the habit starts. The exponential family and the quadratic family come later, and they will get the same three questions.
The parts of this lesson
Each part is its own short page. Go in order, or pick the one you need.
Printables
One page with the family idea, what b and m each do, the special members, parallel lines, and a worked comparison. Plus a worksheet with an answer key and a short lesson plan.