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.
EngageNY
The Graph of a Linear Equation in Two Variables Is a Line
Show your class that linear equations produce graphs of lines. The 20th segment in a unit of 33 provides proof that the graph of a two-variable linear equation is a line. Scholars graph linear equations using two points, either from...
West Contra Costa Unified School District
Sneaking Up on Slope
Pupils determine the pattern in collinear points in order to determine the next point in a sequence. Using the definition of slope, they practice using the slope formula, and finish the activity with three different ways to...
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...
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...
K20 LEARN
Airplanes and Airstrips, Part 2
Table the decision to land. Pupils form flight crews by matching up different representations of linear equations. Given a set of coordinates for an airstrip, the crews determine the equation of the line that will position their planes...
Curated OER
Parallel and Perpendicular Lines
Young geometers get some solid skills practice in evaluating slopes. Beginning with the basics of slope through two points and progressing through properties of parallel and perpendicular lines, the building of skills is gradual and...
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...
Inside Mathematics
Number Towers
Number towers use addition or multiplication to ensure each level is equal. While this is common in factoring, it is often not used with algebraic equations. Solving these six questions relies on problem solving skills and being able to...
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...
Inside Mathematics
Squares and Circles
It's all about lines when going around. Pupils graph the relationship between the length of a side of a square and its perimeter. Class members explain the origin in context of the side length and perimeter. They compare the graph to the...
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...
Georgetown University
Cup-Activity: Writing Equations From Data
Determine how cup stacking relates to linear equations. Pupils stack cups and record the heights. Using the data collected, learners develop a linear equation that models the height. The scholars then interpret the slope and the...
Mathematics Vision Project
Module 7: Connecting Algebra and Geometry
The coordinate plane links key geometry and algebra concepts in this approachable but rigorous unit. The class starts by developing the distance formula from the Pythagorean Theorem, then moves to applications of slope. Activities...
West Contra Costa Unified School District
Discovering Slope of a Line in Standard Form
From start to finish this skills practice resource provides a way for individuals to explore the standard form equation of a line. Begin with a warm-up, work through the problems, and then discover the relationship between the...
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...
Balanced Assessment
All Aboard
Pupils must graph the location of a train using the time given a timetable. They analyze the different legs of the trip, graph the return trip, and compare the two graphs. The lesson ends with a discussion of similarities and...
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...
EngageNY
Making Scale Drawings Using the Parallel Method
How many ways can you create a dilation? Many! Individuals strengthen their understanding of dilations by using various methods to create them. The new technique builds on pupils' understanding of the ratio method. Using the ratio,...
EngageNY
Criterion for Perpendicularity
The Pythagorean Theorem is a geometry pupil's best friend! Learners explain the equation a1b1 + a2b2 = 0 for perpendicular segments using the Pythagorean Theorem. They are able to identify perpendicular segments using their...
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...
Illustrative Mathematics
Slopes and Circles
An upper-level treatment of what is often presented as a basic concept (the right angle of an inscribed circle on the diameter), this activity really elevates the mathematical thought of the learner! Expected to develop formulas...