Here is a resource where algebra learners show their understanding of a system of equations involving a circle and a line. Once graphed, learners see two points of intersection, one where the ordered pair is read, and a second where...

Solving systems of equations underpins much of advanced algebra, especially linear algebra. Developing an intuition for the kinds and descriptions of solutions is key for success in those later courses. This intuition is exactly what...

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...

Get hands on with solving systems of equations graphically. A solid lesson plan uses guided practice to show how to solve systems of linear equations. It allows time for sharing ideas and provides a printable matching activity...

Do you need to graph lines to see the point? A thorough lesson plan provides comprehensive instruction focused on solving systems of equations by graphing. Resources include guided practice worksheet, skill practice worksheet,...

There are many equations Algebra I students are not ready to solve. Graphing to solve gives them a strategy to use when they are unsure of an algebraic approach to solve the problem. The lesson exposes learners to a wide variety of...

Building on knowledge from the previous lesson, the second lesson in this unit teaches scholars to identify and interpret rate of change and initial value of a linear function in context. They investigate how slope expresses the...

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...

What do you get when you cross a circle and a line? One, two, or maybe no solutions! Teach learners to find solutions of quadratic and linear systems. Connect the visual representation of the graph to the abstract algebraic methods. 

You may be able to see patterns visually, but mathematics quantifies them. Here learners find correlation in scatterplots and write equations to represent that relationship. They fit a line to the data, find two points on the line, and...

The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra lesson plan. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching notes and lots...

Represent linear equations in both two and three dimensions using parametric equations. Learners write parametric equations for linear equations in both two and three variables. They graph and convert the parametric equations to...

An intersection is more than just the point where lines intersect; explain this and the meaning of the intersection to your class. The 26th segment in a 33-part series uses graphing to solve systems of equations. Pupils graph linear...

Can you solve an equation graphically? Absolutely! This Algebra II lesson makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through the process of...

Explore how to graph lines from different pieces of information. Scholars learn to graph linear functions when given an equation, given two points that satisfy the function, and when given the initial value and rate of change. They solve...

Pupils work through a guided activity on fitting a linear equation to a set of data by entering the data into a calculator and trying to envision a line of best fit. They then have the calculator determine the least-squares line and...

Although graphing a linear inequality on the plane is but a few steps added onto the graphing of a linear equation, for many learners the logical leap is quite intimidating. This approachable PowerPoint presentation breaks graphing...

Now that learners figured out how to solve for one variable, why not add another? The activity demonstrates, through examples, how to solve a linear system using graphing, substitution, and elimination.

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.

Demonstrate the meaning of an absolute inequality using three different methods. Here, scholars explore absolute value inequalities through graphing, number line distance, and compound inequalities. Pupils complete various activities to...

English and math have more in common than you think. Make a connection between a compound sentence and a compound inequality with an activity that teaches learners the difference between an "and" and "or" inequality through solutions...

Connect linear equations, proportionality, and constant rates of change to linear functions. Young mathematicians learn how linear equations of the form y = mx + b can represent linear functions. They then explore examples of linear...

Can an equation have an infinite number of solutions? Allow your class to discover the relationship between the input and output variables in a two-variable equation. Class members explore the concept through tables and graphs and...

We can mathematically model the path of a robot. Learners use parametric equations to find the location of a robot at a given time. They compare the paths of multiple robots looking for parallel and perpendicular relationships and...