EngageNY
Some Facts About Graphs of Linear Equations in Two Variables
Develop another way to find the equation of a line. The lesson introduces the procedure to find the equation of a line given two points on the line. Pupils determine the two points from the graph of the line.
Willow Tree
Slope
Investigate the different types of slope using graphs and ordered pairs. Scholars use the slope formula to determine the slope of a line between two points. Includes examples with a slope of zero and with no slope. The lesson follows a...
Illustrative Mathematics
Two Lines
Here is a resource that helps your algebra learners understand the connection between the graph of two lines, the equations of lines, and the solutions and intersecting points of lines. It would make a great assessment question, but can...
EngageNY
The Computation of the Slope of a Non-Vertical Line
Determine the slope when the unit rate is difficult to see. The 17th part of a 33-part series presents a situation that calls for a method to calculate the slope for any two points. It provides examples when the slope is hard to...
West Contra Costa Unified School District
Point-Slope Application Problems
Create a linear equation for a problem when the intercept information is not given. The two-day lesson introduces the class to the point-slope form, which can be used for problems when the initial conditions are not provided. Pupils...
EngageNY
The Line Joining Two Distinct Points of the Graph y=mx+b Has Slope m
Investigate the relationship between the slope-intercept form and the slope of the graph. The lesson plan leads an investigation of the slope-intercept equation of a line and its slope. Pupils realize the slope is the same as the...
BW Walch
Creating and Graphing Linear Equations in Two Variables
This detailed presentation starts with a review of using key components to graph a line. It then quickly moves into new territory of taking these important parts and teasing them out of a word problem. Special care is...
Illustrative Mathematics
Find the Change
This exercise is an opportunity for algebra learners to understand the connection between the slope of a line and points found on the line. Use similar triangles to explain why slope m is the same between any two points. Discuss with the...
Teach Engineering
Graphing Equations on the Cartesian Plane: Slope
Slopes are not just for skiing. Instructors introduce class members to the concept of slope and teach them how to calculate the slope from a graph or from points. The lesson also includes the discussion of slopes of parallel and...
EngageNY
The Slope of a Non-Vertical Line
This instructional activity introduces the idea of slope and defines it as a numerical measurement of the steepness of a line. Pupils then use the definition to compare lines, find positive and negative slopes, and notice their...
CCSS Math Activities
Smarter Balanced Sample Items: High School Math – Claim 2
Problem solve across the content standards. The presentation slides provide 19 sample items from the Smarter Balanced high school assessment. Items illustrate Claim 2, problem solving, of the test and are drawn from all the high school...
CK-12 Foundation
Slope: Hiking in the Woods
Learning about slopes from a hike in the woods is a walk in the park. Scholars slide a cutout of a person to simulate a hike along several paths. Passing through indicated points reveals the type of slope (positive, negative, zero, or...
EngageNY
There is Only One Line Passing Through a Given Point with a Given Slope
Prove that an equation in slope-intercept form names only one line. At the beginning, the teacher leads the class through a proof that there is only one line passing through a given point with a given slope using contradiction. The 19th...
Virginia Department of Education
Slope-2-Slope
Pupils build on previous experience with slope to investigate positive, negative, zero, and undefined slope. They complete a puzzle matching slope-intercept and standard forms of linear equations.
Willow Tree
Approximating a Line of Best Fit
You may be able to see patterns visually, but mathematics quantifies them. Here learners find correlation in scatterplots and write equations to represent that relationship. They fit a line to the data, find two points on the line, and...
Virginia Department of Education
Slippery Slope
Explore slope using geometric patterns. Young mathematicians investigate towers built from cubes to develop a linear pattern. They move the data to a coordinate plane to connect the pattern to slopes.
EngageNY
Constant Rates Revisited
Find the faster rate. The resource tasks the class to compare proportional relationships represented in different ways. Pupils find the slope of the proportional relationships to determine the constant rates. They then analyze the...
West Contra Costa Unified School District
Derivative – Standard Definition
Making a clear connection to algebra concepts helps learners understand the definition of a derivative. The lesson plan begins with looking at limits of simple linear and rational functions, and leads to the definition of...
Willow Tree
Equations of a Line
Each form of a linear equation has its purpose — pupils just have to find it. Building on the previous lesson in the series, learners examine point-slope and standard form. Using point-slope form, pupils write the equation of a...
Whitman College
Calculus - Early Transcendentals
This textbook takes the learner from the basic definition of slope through derivatives, integrals, and vector multivariable calculus. Each section is composed primarily of examples, with theoretical introductions and explanations in...
University of Utah
Explore Proportional and Linear Relationships
Progress from proportional relationships to linear functions. Pupils first review concepts of proportionality covered in earlier grades. They then extend these concepts to linear functions, such as determining the slope of a...
Curated OER
Birds' Eggs
More than just data, scatter plots are full of information that can be used to answer a variety of questions. This lesson uses a plot with information about bird egg sizes to answer questions about the relationship between length and...
University of Utah
Representations of a Line
Line up to learn about lines! Scholars discover how to express patterns as linear functions. The workbook then covers how to graph and write linear equations in slope-intercept form, as well as how to write equations of...
Willow Tree
Scatterplots and Stem-and-Leaf Plots
Is there a correlation between the number of cats you own and your age? Use a scatter plot to analyze these correlation questions. Learners plot data and look for positive, negative, or no correlation, then create stem-and-leaf plots to...