# Graphing Lines

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 Original Sim and Translations

### Obsah

• 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!

• 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

 Učitelská příručka (pdf) obsahuje tipy poskytnuté od členů týmu PhET. ( PDF ).

### Teacher-Submitted Activities

Games Remote Lesson ideas Trish Loeblein K-5

ZŠ II.st.
UG-začínající
Remote
Matematika
Fyzika
Chemie
Slope-Intercept Lesson and Activity Sheet Amanda McGarry
ZŠ II.st.
Guided
Remote
Matematika
Slope and Speed (revised) Sarah Borenstein ZŠ II.st. Lab Fyzika
Matematika
Exploring Slope and Speed Sarah Borenstein and Trish Loeblein ZŠ II.st. Lab
Guided
Fyzika
Matematika
Point-Slope Lesson and Activity Sheet Amanda McGarry
ZŠ II.st.
Guided Matematika
Slope Lesson and Activity Sheet Amanda McGarry
ZŠ II.st.
Guided Matematika
Using Transformations to Graph in Slope-Intercept Form Dana Alderman ZŠ II.st.
Guided Matematika
Similar Triangles and Slope Andrew Freeman ZŠ II.st. Guided Matematika
Exploring parallel and perpendicular lines David Schenck
ZŠ II.st.
Guided
Lab
Matematika
Linear Equations in Slope-Intercept and Point-Slope Form using “Graphing Lines PhET Simulation” Enhui Chu
ZŠ II.st.
Guided
Lab
Discuss
Matematika
Making Sense of Slope Jim Freund ZŠ II.st. Guided Matematika
Exploring Solving Systems of Linear Equations Mary Burr ZŠ II.st. Guided
Discuss
Matematika
Go the Distance! Mary Burr ZŠ II.st. Discuss
Guided
Matematika
How do PhET simulations fit in my middle school program? Sarah Borenstein ZŠ II.st. Ostatní Věda o Zemi
Biologie
Chemie
Fyzika
Middle School Math Sim Alignment Amanda McGarry ZŠ II.st. Ostatní Matematika
SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López ZŠ II.st.
Ostatní Matematika
Chemie
Biologie
Fyzika
PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López UG-začínající
Ostatní Chemie
Matematika
Fyzika
PRIMARIA: Alineación con programas de la SEP México (2011 y 2017) Diana López K-5
ZŠ II.st.
Demo

Lab
Discuss
Guided
Fyzika
Matematika
Chemie
Astronomie
Preguntas de razonamiento para todas las simulaciones HTML5 Diana López UG-Pokr
UG-začínající
ZŠ II.st.
K-5

Abs

Discuss
Chemie
Astronomie
Matematika
Fyzika
MS and HS TEK to Sim Alignment Elyse Zimmer
ZŠ II.st.
Ostatní Fyzika
Biologie
Chemie
Physics Graphing and Introduction to Models Steve Banasiak Lab
Fyzika
Mapping of PhET and IBDP Physics Jaya Ramchandani Ostatní Fyzika
Equação e posição das retas Italândia Ferreira de Azevedo e Francisco Régis Vieira Alves Lab Matematika
Estudo da Reta Thamires Silva Aquino de Souza e Francisco Silva Aquino de Souza Guided Matematika
Gráficando Rectas, Gráficando Cuadráticas Andrés Gualberto Palomo Cuevas Remote
Matematika
Explorando sistemas de ecuaciones lineales Mary Burr y Jeffrey Bush, traducido al español por Diana López ZŠ II.st.
Guided Matematika
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Portuguese (Brazil) All português (Brasil) Traçando Retas
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Serbian All Српски Цртање правих
Sinhalese All Sinhalese සරල රේඛීය ප්‍රස්තාර
Slovak All Slovenčina Grafy lineárnej funkcie
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Spanish All español Graficando Rectas
Spanish (Mexico) All español (México) Graficando Rectas
Spanish (Peru) All español (Perú) Graficando Líneas
Spanish (Spain) All español (España) Representando rectas
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Ukrainian All українська Графік лінійної функції
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