various forms of lines
DESCRIPTION
Various Forms of Lines. Slope Intercept Point Slope Form General Form/Standard Form. Slope Intercept Form. y = mx+b m is the slope b is the y intercept How do you find the x intercept? Set y=0 and solve for x. X and Y Intercept. y =.25x-3. Point Slope Form. (y-y 1 )=m(x-x 1 ) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/1.jpg)
Various Forms of Lines
Slope InterceptPoint Slope Form
General Form/Standard Form
![Page 2: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/2.jpg)
Slope Intercept Form
• y=mx+b• m is the slope• b is the y intercept• How do you find the x intercept?– Set y=0 and solve for x
![Page 3: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/3.jpg)
X and Y Intercept
• y=.25x-3
![Page 4: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/4.jpg)
Point Slope Form
• (y-y1)=m(x-x1)• To find x intercept, plug in zero for y• To find y intercept, plug in zero for x
![Page 5: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/5.jpg)
X Intercept
• (y-2)=4(x+3)
![Page 6: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/6.jpg)
Y Intercept
• (y-2)=4(x+3)
![Page 7: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/7.jpg)
Put in Point Slope Form
• Use point slope form of the equation
• Substitute for m, • Solve for y• Slope=-3, Point (-2,4)
![Page 8: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/8.jpg)
Try Another
• Slope=-4, Point (-6, -4)
![Page 9: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/9.jpg)
Basic Review
• Find the slope of the line and write the equation of the line in point slope form
• (-6,3) and (2,-7)• Use the slope formula and the coordinates of
the two points to find the slope
• Use this slope and one of the given points to write the equation of the line
![Page 10: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/10.jpg)
Try Another
• (-9,-2) and (1, -8)
![Page 11: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/11.jpg)
Converting
• You can convert from one form of the equation to another by rearranging terms algebraically to match the general form of the line you are looking for.
![Page 12: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/12.jpg)
Put in slope intercept form
• 2y=4x+2
![Page 13: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/13.jpg)
• 5y=10x+15
![Page 14: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/14.jpg)
• 2y+26=-6x
![Page 15: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/15.jpg)
Converting Point Slope to Slope Intercept
• The rules are the same• Isolate y on the left hand side of the equation• Slope Intercept is really just the simplified
form of point slope
![Page 16: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/16.jpg)
Convert y-2= (x+6)
![Page 17: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/17.jpg)
A little more difficult
• Write the equation of a line with a slope of ½ that goes through (2,3)– Easiest to write in which form first?– Do that, then convert algebraically
![Page 18: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/18.jpg)
Try it!
• Slope of 10, line passing through (3, 34)– Put in slope intercept form
![Page 19: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/19.jpg)
At your seat!
• Convert to slope intercept form1. -3y=-9x-122. Slope of -1 passes through (6,2)3. Slope of 0, passes through (7,5)
![Page 20: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/20.jpg)
Converted from point slope to slope intercept
• You also converted from general form to slope intercept as well.
• More commonly known as standard form but with one small change
![Page 21: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/21.jpg)
Standard Form
• Ax+By=C• Common form of a linear equation, however,
putting in general form is much easier for picking out key information
What is this general form you ask?!!??
![Page 22: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/22.jpg)
General Form
• Ax+By+C=0• X intercept=-C/A• Y intercept=-C/B• Slope=-A/B• How did we figure that out? – By converting from general form to slope
intercept!
![Page 23: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/23.jpg)
First, Practice!
• X intercept, Y intercept
![Page 24: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/24.jpg)
Converting Forms
• Again, really just involves rearranging equations using algebraic operations.
• Look at converting to slope intercept first
![Page 25: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/25.jpg)
General Form to Slope Intercept
• Goal: Isolate y on one side of an equation• Convert by performing inverse operations on
the variable terms and constant terms until y stands alone
![Page 26: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/26.jpg)
Convert 6y+4x-7=0
![Page 27: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/27.jpg)
Converting point slope to general form
• Goal: place x and y on one side of the equation with the constant term on the other side.
• Move the constant term to the left hand side of the equation, making the right hand side 0.
• If any coefficients are fractions, multiply entire equation by the least common denominator of all the fractions.
![Page 28: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/28.jpg)
Convert y+1=(x-2) to general form
![Page 29: Various Forms of Lines](https://reader035.vdocuments.mx/reader035/viewer/2022062315/568161d3550346895dd1cd19/html5/thumbnails/29.jpg)