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...
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 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...
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...
EngageNY
Every Line is a Graph of a Linear Equation
Challenge the class to determine the equation of a line. The 21st part in a 33-part series begins with a proof that every line is a graph of a linear equation. Pupils use that information to find the slope-intercept form of the...
Inside Mathematics
Graphs (2007)
Challenge the class to utilize their knowledge of linear and quadratic functions to determine the intersection of the parent quadratic graph and linear proportional graphs. Using the pattern for the solutions, individuals develop a...
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 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...
Illustrative Mathematics
DVD Profits, Variation 1
The idea in the resource is to understand the connections between proportional relationships, lines, and linear equations. To stay within the context of the standard, skip the part of the resource that solves with unit rates. Instead,...
Balanced Assessment
On Averages and Curves
Determine the average on a curve. The class finds graphical representations of averages and expresses them both symbolically and on the graph. The assessment requires class members to justify using average to describe graphs.
Illustrative Mathematics
Downhill
A car traveling down a steep hill is the model for this resource. The confusion comes when the elevation, E, is given in terms of distance, d. The distance, d, is the horizontal distance from E. Therefore, the equation, E = 7500 – 250d,...
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
Catenary
Develop a model for a hanging chain. Pupils find a mathematical model for a hanging chain and then they compare their models to the precise function that models the curve. Scholars come up with a strategy to determine how close...
Mathematics Assessment Project
College and Career Readiness Mathematics Test C1
Challenge high schoolers with a thorough math resource. The 20-page test incorporates questions from upper-level high school math in applied and higher order questions.
Illustrative Mathematics
Robot Races
Analyze data on a graph to answer three questions after a robot race. Learners practice comparing ratios and reading points on a graph. Answers may vary on the last question based on accuracy of graphing. Use the lesson along with...
Illustrative Mathematics
Sore Throats, Variation 2
What does math have to do with a sore throat? When you mix water and salt you have a great review of how to represent proportional relationships by an equation or graph. Here the proportions of the mixtures may be different, but the...
Inside Mathematics
Swimming Pool
Swimming is more fun with quantities. The short assessment task encompasses finding the volume of a trapezoidal prism using an understanding of quantities. Individuals make a connection to the rate of which the pool is filled with 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...
Khan Academy
Khan Academy: Slope From a Graph
In this exercise, students practice constructing a linear equation for a line graph in order to find the slope. Students receive immediate feedback and have the opportunity to watch a video, get hints, or try questions repeatedly.
Khan Academy
Khan Academy: Algebra I: Slope From Graph
Find the slope of a line on the coordinate plane. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.