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...

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...

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...

If at first you cannot graph, substitute. The lesson plan 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...

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...

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...

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...

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.

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...

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.

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...

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...

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...

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,...

Connect proportional linear equations and systems. The seven-question assessment is the last installment in a 33-part series. The items cover comparing proportional relationships, slope concepts, and simultaneous linear...

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...

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...

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.

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...

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...