Illustrative Mathematics
The Intersection of Two Lines
Here is an introduction to solving simultaneous linear equations. Start by drawing a line through two points. Create a second line which goes through the intersecting point. Background knowledge of how to find the equation of a line and...
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...
College Preparatory Mathematics
Using Elimination To Find the Point of Intersection of Two Lines
Two example problems are solved on the first page using the elimination method with a pair of linear equations. Detailed explanations accompany the math. The second page provides 20 practice problems and their answers. This would be a...
PBS
Plotting Pairs of Coordinate Points in All Four Quadrants to Construct Lines
Your young graphers are motivated by watching three Cyberchase videos to plot points in all four quadrants, connect pairs of points to make a line segment, and find the point of intersection of two lines.
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...
Illustrative Mathematics
Fixing the Furnace
This comprehensive resource applies simultaneous equations to a real-life problem. Though the commentary starts with a graph, some home consumers may choose to begin with a table. A graph does aid learners to visualize the shift of one...
Curated OER
Angles, Lines, and Transversals
Geometers identify and determine angle pair relationships when two parallel lines are intersected by a transversal. They review the concepts of angles by watching streaming video clips online, read definitions of lines and angles from...
Illustrative Mathematics
Cell Phone Plans
Turn your classroom into a local cell phone store. Then, have your cell phone agents use linear equations to visually display three cell plans and their advantages. It makes for a great group project. Discuss how to decide which plan is...
Illustrative Mathematics
Proportional Relationships, Lines, and Linear Equations
The resource is a good introduction to what makes a proportional relationship between two lines. Discuss the similarities of both lines and the possibility of intersection. Use this opportunity to list other acceptable forms of each...
Curated OER
Determining the Point of Intersection Using the TI-83 Plus Calculator
Middle and high schoolers graph two lines and identify the point of intersection of each set of line. They use the TI calculator to help them graph and solve. There are six questions with detailed instruction on how to graph correctly.
NASA
Resolving 2-Plane Traffic Conflicts by Changing Route—Problem Set B
Do pilots create appropriate spacing between aircraft by traveling a longer or shorter path? An interactive presents two airplanes that violate safety protocols. Pupils must determine how to change the path of one plane to create the...
Illustrative Mathematics
Summer Swimming
Here is a real-world application for systems of equations. When is it better to pay an enrollment fee and lower daily rate, and when is it better to pay the regular price? The local swim center is having a special offer, reductions in...
Curated OER
1.2 Points, Lines and Planes
This is a lengthy overview PowerPoint that defines, explains, shows examples, and has practice problems about points, lines and planes. The class will need to write many notes and there is an example of how to set up in the Cornell...
Illustrative Mathematics
Equations of Lines
The intent of this resource is to show algebra learners that there is a proportional relationship between two lines that have an intersecting point. As the coordinate x increases by a constant, the y coordinate also increases. It will...
Curated OER
Points of Intersection
Eighth and ninth graders solve five different problems that include solving two equations. They determine the point of intersection in each of the five pairs of equations given. Pupils define point of intersection as the point where two...
Curated OER
Identifying Linear Functions from Graphs
Keep your mathematicians engaged using this group linear functions activity. Each of ten groups receives two graphs with both an image and equation, as well as a "who has" phrase to call out the next graph. Scholars stay on their toes as...
Curated OER
Skills Review Sheet: Equations
Learners find the equation that passes through two given points. They then locate the intersection of two lines, and find the x and y intercepts for four parabolas when given their equations. Answers are provided.
Charleston School District
Parallel Lines Cut by a Transversal
Pupils study angle measurements between different types of angles associated with parallel lines and transversals. The independent practice asks pupils to identify the types of angles in a diagram and to determine the measure of angles.
Curated OER
Intersections, Unions, and Compound Inequalities
For this algebra worksheet, students graph inequalities on number lines. Two problems are written in interval notation. The other five problems require students to graph and then write in interval notation.
Curated OER
Worksheet 3.5 Simultaneous Equations
In this simultaneous equations worksheet, students solve and complete 7 various types of problems. First, they solve graphically the system of equations shown. Then, students find the number of solutions that each pairs of equations...
EngageNY
Nature of Solutions of a System of Linear Equations
If at first you cannot graph, substitute. The lesson introduces the substitution method as a way to solve linear systems if the point of intersection is hard to determine from a graph. The 28th installment of a 33-part series finishes...
Curated OER
Lines and Line Segments
In this lines and line segments learning exercise, students solve 6 word problems where they identify lines and line segments, draw rectangles made of line segments, and define perpendicular and intersecting lines. The problems require...
Curated OER
Hands On: Construct Parallel and Perpendicular Lines
For this parallel and perpendicular lines worksheet, students solve 6 word problems where they must construct parallel and perpendicular lines, or identify parallel and perpendicular lines in figures. Students must explain the steps used...
Curated OER
Geometry - Angles Overview
Learners address 14 questions that include naming all pairs of opposite and supplementary angles for sets of intersecting lines and then, finding the measure of the unknown angle. They determine the measure of the angle that is...