This lesson 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 definition holds for...

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...

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...

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...

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...

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.

What does slope have to do with lines? Pupils work with lines and determine the slope of the lines informally and with the slope formula. Groups use their knowledge to calculate the slopes of parallel and perpendicular lines. They also...

How many times can eager mathematicians catch the waves? Pupils find the solutions of three different trigonometric equations. They then determine the effect of the slope of a line that intersects a trigonometric function and the number...

Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...

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...

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...

Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.

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...

Algebra and geometry are not interchangeable. Demonstrate why not with a series of problems that deal with the equations of circles and equations of lines that meet specific criteria. 

Don't be a square! Young mathematicians determine the slope and length of a line segment. They then prove whether four given coordinate points form a square.

What if a coordinate plane becomes a slope-intercept plane? What does the graph of a linear function look like? Learners explore these questions by graphing the y-intercept of a linear equation as a function of its slope. The result is a...

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...

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...

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,...

Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.

Young geometers develop one of the fundamental properties of quadrilaterals (connecting side midpoints gives a parallelogram) in this short but thought-provoking exercise. Using a combination of hands-on techniques and abstract algebraic...

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...

This is an interesting geometry problem. Given the figure, find the area of a triangle that is created by the intersecting lines. The solution requires one to use what he/she knows about coordinate geometry, as well as triangle...

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.