Math 1 · Unit 3 · Lesson 2

Slope-Intercept Form: y = mx + b

Every straight line can be written y = mx + b. Two numbers, two jobs: b is the y-intercept, where the line crosses the y-axis and its starting value, because putting x = 0 into the rule leaves y = b. m is the slope, the steepness and direction. Read them off an equation, graph a line from them, and read them off a graph.

About 45 minutes Plot b, step by m, draw the line

The big idea

Every line is y = mx + b, and each of the two numbers has one job. b is the y-intercept, where the line crosses the y-axis, because the y-axis is where x = 0 and putting 0 in for x wipes out the mx part and leaves y = b. So b is the starting value. m is the slope, the rate of change from Lesson 1: every step of 1 to the right changes y by m, so it is the steepness and the direction. Read them off an equation by asking which number is on the x and which stands alone, watching for the invisible 1, a missing b, and a missing x. Graph a line by plotting b first and stepping by m. Read a graph by finding where it crosses the y-axis and counting rise over run. Next lesson, this one form becomes a whole family.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Two numbers, two jobsEvery straight line can be written in one form: 3Read m and b off an equationReading m and b is mostly matching, with a few careful cases. 4Graph a line from its equation: plot b, step by mYou can graph a line straight from its equation, with no table. 5Match it to the graph: pick the one that fits, by eliminationNow the payoff of reading m and b. 6Equation, table, graph: three views of one lineThe equation, the table, and the graph are three views of one line. 7Read the equation off a graphNow go the other way. 8Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the form, the two jobs and why b is on the y-axis, the careful cases, the three graphing moves, and a worked example. Plus a worksheet with grids and an answer key, and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Slope: The Rate of Change Gets Its NameRise over run, the m in this lesson. Next lesson: The Family of LinesOne form, many members: the family of lines. Slide b, tilt m, and learn the habit every later family will use. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.