graphing linear equations
DESCRIPTION
Graphing Linear Equations. Graphing Linear Equations. Linear equation: an equation with two variables that are both to the first power . Ex. x + y = 3 The graph of a linear equation will always be a straight line. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/1.jpg)
Graphing Linear Equations
![Page 2: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/2.jpg)
Graphing Linear Equations
• Linear equation: an equation with two variables that are both to the first power.
Ex. x + y = 3
• The graph of a linear equation will always be a straight line.
![Page 3: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/3.jpg)
• Previously, you’ve solved equations that contain just one variable. For example, let’s solve:
2x + 3 = 7
![Page 4: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/4.jpg)
• Linear equations have an infinite number of solutions.
• When we solve a linear equation, we get a list of ordered pairs.
• The graph of all of the ordered pairs creates a straight line.
![Page 5: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/5.jpg)
x + y = 3
x y
![Page 6: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/6.jpg)
Ordered Pairs
![Page 7: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/7.jpg)
Horizontal and Vertical Lines
• Sometimes, the graph of an equation is a horizontal or a vertical line.
• If our equation only contains a “y”, then our graph is a horizontal line.
• If our equation only contains an “x”, then our graph is a vertical line.
![Page 8: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/8.jpg)
Example
y = 3x y
1 3
3 3
-1 3
0.5 3
-3 3
![Page 9: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/9.jpg)
Example
x = 3x y
3 2
3 1
3 -4
3 0.5
3 3
![Page 10: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/10.jpg)
ExamplesFor each of the following linear equations:a) Find four ordered pair that complete the equationb) Plot the ordered pairs on a coordinate plane
1) x + y = 6
2) y = x + 1
3) x = 4
![Page 11: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/11.jpg)
Ordered Pairs
x + y = 6
x y
![Page 12: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/12.jpg)
Ordered Pairs
Y = x + 1
x y
![Page 13: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/13.jpg)
Ordered Pairsx = 2
x y
![Page 14: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/14.jpg)
Slope
• Slope: A number which is used to indicate the steepness of a line, as well as indicating whether the line is tilted uphill or downhill.
• Think of a road going uphill (or downhill). The steepness of the road is the slope.
![Page 15: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/15.jpg)
![Page 16: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/16.jpg)
The slope we are studying is associated with the graph of a line.
![Page 17: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/17.jpg)
Steepness
![Page 18: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/18.jpg)
Vertical ChangeHorizontal Change
This ratio is also known asRiseRun
![Page 19: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/19.jpg)
Graph (3,2) and (-1,-1)
![Page 20: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/20.jpg)
Draw a line through the points.
![Page 21: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/21.jpg)
Now that we have our line lets find its slope.
Remember we are finding the following ratio:Vertical or Rise
Horizontal Run
![Page 22: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/22.jpg)
Vertical Changeor the Rise
3
![Page 23: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/23.jpg)
Horizontal Changeor the Run
4
3
![Page 24: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/24.jpg)
Vertical Rise Horizontal Run
34
![Page 25: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/25.jpg)
Find the slope of the following line.
![Page 26: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/26.jpg)
The slope is…
12
![Page 27: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/27.jpg)
Find the slope of the line.
![Page 28: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/28.jpg)
The slope is….
-3
![Page 29: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/29.jpg)
Find the slope of these lines.
![Page 30: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/30.jpg)
The slope is…
• Black line 3
• Red Line 1
• Blue Line -1/2
![Page 31: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/31.jpg)
Find the slope of these lines
![Page 32: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/32.jpg)
The slope is…
• Orange line 0
• Green Line Undefined
![Page 33: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/33.jpg)
• Let’s go back to our first example.• Graph the line that goes through (3,2) and (-1,-1)
![Page 34: Graphing Linear Equations](https://reader035.vdocuments.us/reader035/viewer/2022062301/568161e6550346895dd20a5a/html5/thumbnails/34.jpg)
Equation
(3,2) and (-1,-1)