Linear Equations

Use Words

100

m=(y₂-y₁)/(x₂-x₁)

slope is equal to the change in y divided by the change in x

200

( (x₁+x₂)/2 , (y₁+y₂)/2 )

What is the midpoint formula?

or 

(average x,  average y) is the midpoint of the segment with the endpoints of (x₁, y₁) and (x₂, y₂)

300

d=sqrt[(change in x)² + (change in y)²]

What is the distance formula?

400

line 1: m=-5

line 2: m=-5

line 1 is parallel to line 2

500

line 1:m=2

line 2: m=-1/2

line 1 is perpendicular to line 2

Slope-intercept

100

What is the slope-intercept form?

y=mx+b

200

What does each variable in the equation mean?

y=mx+b

y is the y coordinate

x is the x coordinate

m is slope

b is the y-intercept

300

What are the three ways to find/think about slope?

rise/run
(y₂-y₁) / (x₂ - x₁)

(change in y) / (change in x)

400

Write the equation of the line that contains the 

point (3, -2) and has the slope m=-2  

in slope intercept form

y= -2x +4

500

Write equation of the line that contains the ordered pairs 

(2,5) , (-4,13) 

in slope-intercept form

slope: -4/3

b: 23/3

y = -4/3x + 23/3

Standard Form

100

What is the standard form?

Ax+By=C

200

How can you find the x and y intercepts using the standard form?

What is the "cover up" method?

300

Write y=-2/3 x +10 in standard form.

2x+3y=10

400

Calculate the slope and intercepts for

2x+5y=10

slope: -2/5

x-intercept: (5,0)

y-intercept: (0,2)

500

What are the 4 constraints of standard form? 

(related to the A, B, C)

A must be positive

A, B, C must be integers

A and B can not be zero

LCM

Point-slope

100

What is the point-slope form?

y-y₁=m(x-x₁)

200

Give a point on the line and the slope of the line whose equation is below.

y-2 = 3(x+5)

m=3

 and (-5, 2)

300

Write the equation of the line that contains the points (5,0) , (3,1)

in point-slope form.

y+0 = -1/2(x-5)

or y-1 = -1/2(x-3)

400

Write the equation of the line that contains the points (5, -4) , (-1, -1)

in point-slope form.

y+4 = -1/2 (x-5)

or

y+1 = -1/2 (x+1)

500

What is the ordered pair of the equation?

y - 3 = 7/8 (x+2)

(-2 , 3)

Converting

100

Convert to standard form

y=-2x + 5

2x + y = 5

200

Convert to slope intercept

2x+3y=-6

y = -2/3x -2

300

Convert to slope intercept

y-3 = 6/5(x-5)

y= 6/5x - 3

400

Convert to slope intercept

y-8 = 3/4 (x+12)

y-8 = 3/4x + 9

y = 3/4x + 17

500

Convert to standard form

y+4 = -5/2(x-2)

5x+2y=2