Slope Concepts Collection

Linear Functions

An identity function is a linear function of the form f(x) = x, where the output is equal to the input for all values of x.

Linear Functions

An increasing linear function is a linear function where the slope is positive, indicating that as the input value increases, the output value also increases.

Linear Functions

A linear function is a function that can be graphed as a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Linear Functions

Point-slope form of a linear equation is written as y − y1 ​ = m(x−x1​ ), where m is the slope and (x1 ​ ,y1​) is a point on the line.

Linear Functions

Rate of change in a linear function is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope m in the equation y = mx + b.

Linear Functions

Slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

Linear Functions

The equation of a line from two coordinates can be determined by finding the slope between the two points and using it in the point-slope form of a linear equation.

Linear Functions

The x-intercept is the point where a graph crosses the x-axis, indicating the value of x when 𝑦 y is zero.

Linear Functions

The y-intercept is the point where a graph crosses the y-axis, indicating the value of y when x is zero.

Slope

Delta x is the change in the x-coordinate in a linear relationship.

Slope

Delta y is the change in the y-coordinate in a linear relationship.

Slope

Grade is a ratio indicating the steepness of a slope.

The term Grade commonly refers to the angle of elevation or slope expressed as a percentage. In engineering, grades are crucial for designing roads and railways, ensuring safety and efficiency.

Slope

Gradient represents the rate of change of a quantity.

Slope

Negative Slope indicates a decrease in value as x increases.

Slope

Pitch refers to the steepness of a slope in a real-world context.

Pitch is commonly applied in construction and design fields to denote the angle of roofs and ramps. This is essential in architecture, especially when dealing with drainage and material use.

Slope

Point-Slope Form is a way to express linear equations given the slope and a point on the line.

Slope

Positive Slope indicates an increase in value as x increases.

The Positive Slope indicates that as x grows, y also rises, signifying direct relationships in data analysis. This principle enables predictions in various analytics and trends.

Slope

Slope measures the steepness of a line.

Slope is a fundamental concept in mathematics, expressing the ratio of vertical rise to horizontal run. This is vital for understanding linear functions, essential in fields such as physics, economics, and data science.

Slope

The Slope Formula calculates the rate of change.

The Slope Formula is typically represented as 

Slope

The slope-intercept form is an equation of a straight line represented as y = m x + b, where m is the slope and b is the y-intercept.

Slope

Parallel lines are lines in the same plane that never meet; they have equal slopes.

Slope

Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other.

Slope

Steepness is a measure of how steep a line is, typically calculated as the absolute value of the slope.

Slope

The rise over the run describes the change in y over the change in x in a linear relationship.

Slope

Undefined slope occurs when a vertical line is present, meaning there is no change in x.

Slope

Zero slope describes a horizontal line where there is no change in y as x changes.

In this graphing calculator activity, have your students explore how to convert linear equations in point-slope to a linear function in slope-intercept form.

In this graphing calculator activity, have your students explore how to convert linear equations in point-slope to a linear function in slope-intercept form. This Desmos template allows students to explore the effect of changes in the values of coordinates of the point and the slope of the line. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear equations and functions.

Related Resources

To see additional resources on this topic click on the Related Resources tab above.

Desmos Collection

In this graphing calculator activity, have your students explore linear functions of the form y = mx. This Desmos template allows students to explore the effect of changes in the slope have on the graph of the line.

In this graphing calculator activity, have your students explore linear functions of the form y = mx. This Desmos template allows students to explore the effect of changes in the slope have on the graph of the line. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear functions.

Note: The download is a PDF worksheet.

Related Resources

To see additional resources on this topic click on the Related Resources tab above.

Desmos Collection

In this graphing calculator activity, have your students explore linear functions of the form y = x + b. This Desmos template allows students to explore the effect of changes in the y-intercept have on the graph of the line.

In this graphing calculator activity, have your students explore linear functions of the form y = x + b. This Desmos template allows students to explore the effect of changes in the y-intercept have on the graph of the line. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear functions.

Note: The download is a PDF worksheet.

Related Resources

To see additional resources on this topic click on the Related Resources tab above.

Desmos Collection

In this graphing calculator activity, have your students explore linear functions of the form y = mx + b.

In this graphing calculator activity, have your students explore linear functions of the form y = mx + b. This Desmos template allows students to explore the effect of changes in the slope (m) and the y-intercept (b) have on the graph of the line. A companion downloadable worksheet uses the graphing calculator template to explore the properties of these linear functions. Note: The download is a PDF worksheet. Related Resources To see additional resources on this topic click on the Related Resources tab above.

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit.

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost.

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity.

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity. In the activity students click on the points to create a line segment connecting two points. Use the background grid to determine the rise and the run and calculate the slope.

Desmos Activity: Slope As Rise Over Run 2

In this activity, students input different values for the coordinates to create a new line. They can then measure the rise and run to calculate the slope.

Desmos Activity: Slope As Rise Over Run 2

In this activity, students input different values for the coordinates to create a new line. They can then measure the rise and run to calculate the slope.

The formula for the Slope Formula. This is part of a collection of math formulas. 

The formula for the Slope Formula. This is part of a collection of math formulas. 

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

Learn different strategies for finding the slope of a line.

Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age.

In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking.

In this Slide Show, use the Desmos graphing calculator to explore the point-slope form.

In this Slide Show, use the Desmos graphing calculator to explore the point-slope form. To see the complete collection of Desmos Resources click on this link.

In this Slide Show, use the Desmos graphing calculator to explore linear equations in slope intercept form.

In this Slide Show, use the Desmos graphing calculator to explore linear equations in slope intercept form. To see the complete collection of Desmos Resources click on this link.

In this Slide Show, learn how graph data in a scatterplot using the graph window. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, learn how graph data in a scatterplot using the graph window. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, create a template for determining the equation of a line given a point and the slope of the line. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, create a template for determining the equation of a line given a point and the slope of the line. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to calculate the slope of the line between two points.

In this Slide Show, the Graph Window is used to calculate the slope of the line between two points.

In this Slide Show, the Graph Window is used to construct two points and a linked formula to calculate the slope. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, the Graph Window is used to construct two points and a linked formula to calculate the slope. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, a Slope Formula template is created using the Spreadsheet window. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, a Slope Formula template is created using the Spreadsheet window. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, linear functions in slope-intercept form are graphed using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

In this Slide Show, linear functions in slope-intercept form are graphed using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

<h1>INSTRUCTIONAL RESOURCE: Tutorial: The Point-Slope Form</h1><p>In this Slide Show, learn about thepoint-slope form. </p><h3>

<h1>INSTRUCTIONAL RESOURCE: Tutorial: The Point-Slope Form</h1><p>In this Slide Show, learn about thepoint-slope form. </p><h3> This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, <a href="https://www.media4math.com/instructional-resources?field_la_display_tit… on this link.</u></strong></a> </h3>

This slide show shows the structure of a linear function.

This slide show shows the structure of a linear function. In particular, the slide show focuses on: How the parameters of a linear function affect its graph; analyzing a linear function based on its parameters.

In this Slide Show, learn how to use the TI-Nspire CX to calculate slope. Note: The download is a PPT file.

In this Slide Show, learn how to use the TI-Nspire CX to calculate slope. Note: The download is a PPT file.

This slide show shows how to write equations in slope-intercept form for parallel and perpendicular lines.

This slide show shows how to write equations in slope-intercept form for parallel and perpendicular lines. This slide show also includes some sample SAT-style questions.

INSTRUCTIONAL RESOURCE: Tutorial: Point-Slope Form (SAT Prep)

INSTRUCTIONAL RESOURCE: Tutorial: Point-Slope Form (SAT Prep)

This slide show shows how to use the point-slope form to write a linear equation in slope-intercept form. This slide show also includes some sample SAT-style questions.

In this Slide Show, learn about the slope-intercept form.

In this Slide Show, learn about the slope-intercept form.

In this Slide Show, learn how to use the slope formula.

In this Slide Show, learn how to use the slope formula.

This interactive crossword puzzle tests knowledge of key terms on the topic of the slope intercept form.

This interactive crossword puzzle tests knowledge of key terms on the topic of the slope intercept form.

Use this Jeopardy-style math game to review linear functions.

Use this Jeopardy-style math game to review linear functions. This Jeopardy game has a bank of hundreds of questions for thousands of unique game experiences. To see the complete set of Math Games and Puzzles, click on this link.

In this drag-and-drop game, match the coordinates with the equation of the line that crosses these points.

In this drag-and-drop game, match the coordinates with the equation of the line that crosses these points. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

In this drag-and-drop game, match the linear equation with the equation of a parallel line through a given point.

In this drag-and-drop game, match the linear equation with the equation of a parallel line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

In this drag-and-drop game, match the linear equation with the equation of a perpendicular line through a given point.

In this drag-and-drop game, match the linear equation with the equation of a perpendicular line through a given point. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

In this drag-and-drop game, match the linear equation in point-slope form with its slope-intercept counterpart.

In this drag-and-drop game, match the linear equation in point-slope form with its slope-intercept counterpart. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

In this drag-and-drop game, match the coordinates to the slope of the line that passes through the two points.

In this drag-and-drop game, match the coordinates to the slope of the line that passes through the two points. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format.

Use this math game to review linear functions in slope-intercept form.

Use this math game to review linear functions in slope-intercept form.