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. 

Graph linear equations in standard form with one coefficient equal to zero. The lesson plan reviews graphing lines in standard form and moves to having y-coefficient zero. Pupils determine the orientation of the line and, through a...

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...

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 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...

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...

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...

Add more points on the graph ... and it still remains a line! The 13th installment in a series of 33 leads the class to the understanding that the graph of linear equation is a line. Pupils find several solutions to a two-variable linear...

When told to describe a line, do your pupils list its color, length, and which side is high or low? Use a learning exercise that engages scholars to properly label line graphs. It then requests two applied reasoning answers.

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...

They appear to be different, yet they are the same line. Part 24 out of 33 lessons provides a theorem about the relationships of coefficients of equivalent linear equations. Pupils use the theorem to determine whether two equations are...

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...

What do a line and an ellipse have in common? Maybe zero, one, or two points! Learners consider the equation of an ellipse and a line to determine if their graphs have any shared points. They then write a system of equations, including...

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...

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...

A line is a line is a line. As a middle school assessment task, learners first identify graphs of given linear equations. They then identify the equations that represent real-world situations.

Create an understanding of solving problems that require more than one equation. The lesson plan introduces the concept of systems of linear equations by using a familiar situation of constant rate problems. Pupils compare the graphs of...

The intent of this resource is to show algebra learners that there is a proportional relationship between two lines that have an intersecting point. As the coordinate x increases by a constant, the y coordinate also increases.  It...

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...

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...

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...

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...

Develop graphs by following the pattern. The resource provides opportunities for reviewing graphing linear equations. Pupils create tables to graph linear equations by using patterns whenever possible. The activity and video are part of...

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.