Math 1 · Unit 3

Linear Functions

Six lessons: slope, slope-intercept form, the family of lines, writing the equation of a line, linear functions in the real world, and other forms of a line. Each card below opens a lesson. Every lesson has practice with hints, a study guide, a worksheet with an answer key, and a lesson plan.

6 lessons Back to the Math 1 map

Unit 3 · Lesson 1 · The rate of change gets its name

Slope: The Rate of Change Gets Its Name

The rate of change from Unit 2 gets its name. Slope is rise over run: the top is how much y went up or down, the bottom is how far you went right. Count it on a graph, read it from a table, or subtract from two points. Positive climbs, negative falls, zero is flat.

Start Unit 3, Lesson 1

Unit 3 · Lesson 2 · y = mx + b

Slope-Intercept Form: y = mx + b

The heart of the unit: y = mx + b. b is the y-intercept, where the line crosses the y-axis, because that is where x = 0. m is the slope, the steepness and direction. Read them off an equation, graph a line by plotting b and stepping by m, and read them back off a graph.

Start Unit 3, Lesson 2

Unit 3 · Lesson 3 · A family of graphs

The Family of Lines: One Form, Many Members

All lines share one form, y = mx + b, so they are one family, and each line is a member picked out by its m and b. Slide b and the line moves up or down. Change m and it tilts around its y-intercept. Move the sliders yourself, match equations to graphs, and meet the question every later family will get.

Start Unit 3, Lesson 3

Unit 3 · Lesson 4 · From anything to y = mx + b

Writing the Equation of a Line

Write y = mx + b from whatever you are given: a graph, a table, two points, or a slope and a point. Find m, find b, write it, check it on the grid. Then the x-intercept, where the line crosses the x-axis because y is 0, and what it means in a story.

Start Unit 3, Lesson 4

Unit 3 · Lesson 5 · Rates, starts, and comparisons

Linear Functions in the Real World

Read m and b in a story: b is the starting amount or flat fee, m is the per-hour, per-month, per-mile rate. Write the model and use it. Test whether a situation is linear with the constant-difference check. Then compare two linear functions given in different ways: which starts higher, which grows faster, when they are equal.

Start Unit 3, Lesson 5

Unit 3 · Lesson 6 · Standard form and point-slope form

Other Forms of a Line

An optional short lesson. Standard form, Ax + By = C, finds both intercepts fast. Point-slope form is a shortcut from a slope and a point. Either way, the main move is to rewrite into y = mx + b and read m and b.

Start Unit 3, Lesson 6

Printables for Unit 3

Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.

Where this goes next

Previous: Unit 2, Introduction to Functions and Graph BehaviorsSix lessons: what a function is, from points to a line, domain and range, reading a graph, graphing stories, and average rate of change. Next: Unit 4, Parallel and Perpendicular LinesFour lessons: one idea, the slope, doing two new jobs. Back to the Math 1 mapAll fifteen units, in course order.