Math 1 · Unit 3 · Lesson 4

Writing the Equation of a Line

Whatever you are handed, the job is the same: find m, the slope, find b, the y-intercept, and write y = mx + b. From a graph, from a table, from two points, or from a slope and a point. Then meet the other crossing, the x-intercept, where y is 0.

About 45 minutes Find m, find b, write it

The big idea

Every line is y = mx + b, so writing its equation is always the same two finds. Find m, the slope: count rise over run on a graph, read the constant change in a table, or subtract two points. Find b, the y-intercept: read it where the line crosses the y-axis, take the x = 0 row of a table, or put one known point into y = mx + b and solve the one-step equation for b. Then write it and check with a point. The x-intercept is the other crossing: put y = 0 in and solve for x. In a story, b is the starting amount and the x-intercept is when the story reaches zero.

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 2Find m, find b, write itLesson 2 read m and b off an equation. 3The four starting points, workedThe line crosses the y-axis at (0, −2), so b = −2. 4The other crossing: the x-interceptb is where the line crosses the y-axis, the y-intercept, the value when x is 0. 5Check your line on the gridTwo lines from the practice. 6Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the four starting points, the put-the-point-in move, both intercepts, and a worked two-point example. Plus a worksheet with 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: The Family of Lines: One Form, Many MembersThe form every line is written in. Next lesson: Linear Functions in the Real Worldm becomes a rate and b becomes a starting amount. Build the model, test for linear, and compare two plans. 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.