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
Various Forms of Lines
Slope InterceptPoint 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-y1)=m(x-x1)• To find x intercept, plug in zero for y• To find y intercept, plug in zero for x
X Intercept
• (y-2)=4(x+3)
Y Intercept
• (y-2)=4(x+3)
Put in Point Slope Form
• Use point slope form of the equation
• Substitute for m, • Solve for y• Slope=-3, Point (-2,4)
Try Another
• Slope=-4, Point (-6, -4)
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
Try Another
• (-9,-2) and (1, -8)
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.
Put in slope intercept form
• 2y=4x+2
• 5y=10x+15
• 2y+26=-6x
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
Convert y-2= (x+6)
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
Try it!
• Slope of 10, line passing through (3, 34)– Put in slope intercept form
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)
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
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?!!??
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!
First, Practice!
• X intercept, Y intercept
Converting Forms
• Again, really just involves rearranging equations using algebraic operations.
• Look at converting to slope intercept first
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
Convert 6y+4x-7=0
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.
Convert y+1=(x-2) to general form