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...

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 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...

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...

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...

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...

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...

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...

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 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,...

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...

Your algebra learners explore linear functions concretely using tables of values in a collaborative task. The idea that linear function values change by equal differences over equal intervals, is emphasized. The slope and...

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...

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...

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...

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...

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. 

According to the resource graph, which costs more: peaches or plums? Algebra learners compare two proportional relationships and then throw in a banana. Leaving out the scale helps students become intuitive about graphing. 

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...

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)

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...

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...

A car traveling down a steep hill is the model for this resource. The confusion comes when the elevation, E, is given in terms of distance, d. The distance, d, is the horizontal distance from E. Therefore, the equation, E = 7500 – 250d,...

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.