Graphing Lines

Graphing Lines Screenshot
  • Graphing Linear Equations
  • Lines
  • Slope
Java Logo Original Sim and Translations

Topics

  • Graphing Linear Equations
  • Lines
  • Slope

Description

Explore the world of lines. Investigate the relationships between linear equations, slope, and graphs of lines. Challenge yourself in the line game!

Sample Learning Goals

  • Explain how the slope of a graphed line can be computed.
  • Graph a line given an equation in either slope-intercept or point-slope form.
  • Write an equation in slope-intercept or point-slope form given a graphed line.
  • Predict how changing variables in a linear equation will affect the graphed line.

Standards Alignment

Common Core - Math

8.EE.B.5
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.EE.B.6
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.C.8a
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
8.EE.C.8b
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
8.F.A.3
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
HSF-IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
HSF-IF.C.7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
HSF-LE.A.1a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Version 1.3.10

Teacher Tips

Download teacher tips PDF Overview of sim controls, model simplifications, and insights into student thinking ( PDF ).

Teacher-Submitted Activities

Games Remote Lesson ideas A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Trish Loeblein HS
MS
UG-Intro
K-5
Remote
HW
Chemistry
Mathematics
Physics
Slope-Intercept Lesson and Activity Sheet A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Amanda McGarry HS
MS
Remote
Guided
Mathematics
Slope and Speed (revised) A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Sarah Borenstein MS Lab Physics
Mathematics
Exploring Slope and Speed A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Sarah Borenstein and Trish Loeblein MS Guided
Lab
Mathematics
Physics
Point-Slope Lesson and Activity Sheet A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Amanda McGarry HS
MS
Guided Mathematics
Slope Lesson and Activity Sheet A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Amanda McGarry MS
HS
Guided Mathematics
Using Transformations to Graph in Slope-Intercept Form A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Dana Alderman HS
MS
Guided Mathematics
Similar Triangles and Slope A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Andrew Freeman MS Guided Mathematics
Exploring parallel and perpendicular lines A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. David Schenck MS
HS
Guided
Lab
Mathematics
Linear Equations in Slope-Intercept and Point-Slope Form using “Graphing Lines PhET Simulation” A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Enhui Chu HS
MS
Lab
Discuss
Guided
Mathematics
Making Sense of Slope A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Jim Freund MS Guided Mathematics
Exploring Solving Systems of Linear Equations A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Mary Burr MS Guided
Discuss
Mathematics
Go the Distance! A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Mary Burr MS Guided
Discuss
Mathematics
How do PhET simulations fit in my middle school program? This contribution was designed by PhET. Sarah Borenstein MS Other Biology
Chemistry
Earth Science
Physics
Middle School Math Sim Alignment This contribution was designed by PhET. Amanda McGarry MS Other Mathematics
Physics Graphing and Introduction to Models Steve Banasiak HS Lab
HW
Physics
Mapping of PhET and IBDP Physics Jaya Ramchandani HS Other Physics
MS and HS TEK to Sim Alignment Elyse Zimmer HS
MS
Other Physics
Biology
Chemistry
Preguntas de razonamiento para todas las simulaciones HTML5 A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. This contribution was designed by PhET. Diana López UG-Intro
K-5
MS
Grad
HS
UG-Adv
HW
Discuss
Physics
Mathematics
Astronomy
Chemistry
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López MS
HS
Other Chemistry
Mathematics
Biology
Physics
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) This contribution was designed by PhET. Diana López UG-Intro
HS
Other Chemistry
Physics
Mathematics
PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) This contribution was designed by PhET. Diana López K-5
MS
Discuss
Lab
Guided
Demo
HW
Mathematics
Chemistry
Physics
Astronomy
Equação e posição das retas Italândia Ferreira de Azevedo e Francisco Régis Vieira Alves HS Lab Mathematics
Estudo da Reta Thamires Silva Aquino de Souza e Francisco Silva Aquino de Souza HS Guided Mathematics
Gráficando Rectas, Gráficando Cuadráticas Andrés Gualberto Palomo Cuevas HS Remote
HW
Mathematics
Explorando sistemas de ecuaciones lineales Mary Burr y Jeffrey Bush, traducido al español por Diana López MS
HS
Guided Mathematics

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iPad:
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Android:
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Chromebook:
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Macintosh Systems:
macOS 10.9.5+, Safari 9+, latest version of Chrome.

Linux Systems:
Not officially supported. Please contact phethelp@colorado.edu with troubleshooting issues.

Design Team Third-party Libraries Thanks To
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  • Patricia Loeblein
  • Amanda McGarry
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  • Sharon Siman-Tov (graphic arts)
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