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...

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...

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.

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...

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...

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.

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...

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)

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...

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...

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. 

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...

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 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...

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...

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,...

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...

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,...

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...

Making money is important to teenagers. It is up to your apprentices to determine how much two wage earners make with their after school jobs. Participants work with a table, an equation, and a graph and compare the two workers to see...

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.

Introduce your algebra learners to linear and quadratic functions. Learners compare the differences and relate them back to the equations and graphs. Lead your class to discussions on the properties of a function or a constant slope...