Linear Equations

Random

100

What century did linear algebra begin?

Late 17th century

200

Who is said to have originated linear equations? 

Leibniz

300

How many types of algebra are there?

Bonus: name the types

Elementary, abstract, advanced, communicative, and linear

400

Who discovered the pythagorean theorem?

Not Pythagoras, the Babylonians

500

What is Ms. Tong's favorite algebraic formula?

Quadratic Formula

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 slope?

rise/run
(y₂-y₁) / (x₂ - x₁)

(change in y) / (change in x)

400

Write in slope intercept form

(3, -2) m=-2

y= -2x +4

500

Write the ordered pairs in slope-intercept form
(2,5) , (-4,13)

slope: -4/3

b: 23/3

y = -4/3x + 23/3

Standard Form

100

What is the standard form?

Ax+By=C

200

What are the 4 rules of standard form? 

A must be positive

A, B, C must be integers

A and B can not be zero

LCM

300

What are the formulas to calculate: slope, y-intercept, and x-intercept?

slope: -A/B

y-intercept: C/B

x-intercept: C/A

400

Calculate the slope and intercepts for

2x+5y=10

slope: -2/5

x-intercept: (5,0)

y-intercept: (0,2)

Point-slope

100

What is the point-slope form?

y-y₁=m(x-x₁)

200

What is the ordered pair of the equation?

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

(-2 , 3)

300

Write in point slope (5,0) , (3,1)

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

400

(5, -4) , (-1, -1)

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

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