Lesson 11Writing Equations for Lines
Learning Goal
Let’s explore the relationship between points on a line and the slope of the line.
Learning Targets
I can decide whether a point is on a line by finding quotients of horizontal and vertical distances.
Lesson Terms
- similar
- slope
Warm Up: Coordinates and Lengths in the Coordinate Plane
Problem 1
Find each of the following and explain your reasoning:
The length of segment
. The coordinates of
.
Activity 1: What We Mean by an Equation of a Line
Problem 1
Line
What are the coordinates of
and ? Is point
on line ? Explain how you know. Is point
on line ? Explain how you know. Is point
on line ? Explain how you know. Suppose you know the
- and -coordinates of a point. Write a rule that would allow you to test whether the point is on line .
Activity 2: Writing Relationships from Slope Triangles
Problem 1
Here are two diagrams:
Complete each diagram so that all vertical and horizontal segments have expressions for their lengths.
Use what you know about similar triangles to find an equation for the quotient of the vertical and horizontal side lengths of
in each diagram.
Are you ready for more?
Problem 1
Find the area of the shaded region by summing the areas of the shaded triangles.
Find the area of the shaded region by subtracting the area of the unshaded region from the large triangle.
What is going on here?
Lesson Summary
Here are the points
The slope for triangle
Since
Here are two different slope triangles. We can use the same reasoning to describe the relationship between
The slope for triangle
Since