Algebra 1 Lesson

Point-Slope Form: From a Point and a Slope to Every Form

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9th GradeBTC Style / Thinking Classrooms50 min

Learning Objective

Students will write linear equations in point-slope form given a point and a slope, convert between point-slope, slope-intercept, and standard forms, and write equations given two points.

Lesson Overview

Students discover point-slope form by reasoning from what they already know about slope, then practice writing, interpreting, and converting equations through a thin-sliced progression that changes exactly one variable at a time.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (at least 2 colors per group)
Pencils and scratch paper

Scaffolded Task Progression

1Task 1

A line has slope

m = 2

and passes through the point

(0, 5)

.

1. Write the equation in slope-intercept form.
2. Now look at the slope formula:

\frac{y - 5}{x - 0} = 2

. Simplify this equation. What do you notice?

2Task 2

A line has slope

m = 2

and passes through the point

(3, 5)

.

Write the equation in point-slope form:

y - y_{1} = m (x - x_{1})

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