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