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...

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...

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...

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...

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...

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.

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.

This is a great exercise in graphing proportional quantities to interpret the unit rate as the slope of a graph. It is not easy for learners to understand what a unit rate is. When it is presented as the slope of a linear line graph,...

The slope makes a difference. Given an equation of a circle and point, scholars determine the relationship of the slope of a line through the point and the number of intersections with the circle. After graphing the relationship, pupils...

Your algebra learners write linear, exponential, and quadratic equations containing the same two graph points in this collaborative task.

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...

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...

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...

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...

Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

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...

Your learners will explore linear functions by analyzing a graph of the linear equations.Then learners analyze through calculating f(x+P) and g(x+p)

Compare two different proportional relationships on a graph. It is up to your mathematicians to determine which of two moving objects have greater speed. A good example of a Common Core multiple choice question. 

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...

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...

The AP® exam is not just about the calculations. By reviewing the free-response questions from 2008, teachers and pupils see that several items require justifications and explanations to gain full credit. The chief reader even points out...

Grab a peak inside the test. The 2005 free-response questions from the AP® Calculus exam allow learners to see how topics appear on the tests. Topics cover differential equations, bounded areas, particle motion, and slopes of tangent lines.