6-11 Graphing

Question 1

Why is the x-y plane called the Cartesian plane?

Answer 1

It was developed by Descartes

Question 2

What did the Cartesian plane do?

Answer 2

It united algebra and geometry

Question 3

What is the origin?

Answer 3

It is where the x and y axes meet.

Question 4

What is an ordered pair made of?

Answer 4

and x-coordinate (abscissa)

and a y-coordinate (ordinate)

Question 5

What is a linear equation?

Answer 5

An equation with the highest power of 1

Question 6

How do you find the inverse of a function?

Answer 6

(1) Exchange the x and y.
(2) Solve for y.

Question 7

What are the 3 types of linear equations?

Answer 7

(1) Has exactly 1 solution.
(2) Has no solutions.
(3) It is an identity.

Question 8

What is the slope of an equation?

Answer 8

^{rise (▲y)} / _{run (▲x)}

Question 9

What is the slope of a horizontal line?

Answer 9

Zero.

Question 10

What is the slope of a vertical line?

Answer 10

Undefined. You can’t divide by 0.

Question 11

What is the slope-intercept form of a linear equation?

Answer 11

y = mx + b

m = slope

b = y-intercept

Question 12

What is the point-slope form of a linear equation?

Answer 12

(y - y₁) = m(x - x₁)

Question 13

Given 2 points and the slope, how do you find the y-intercept using the point-slope form?

Answer 13

Put it in slope-intercept form?

Question 14

Given points (3,2) and (-1,-5) and slope ⁷/₄, what is the y-intercept?

Answer 14

(y - 2) = ⁷/₄(x - 3)

y = ⁷/₄x -²¹ /₄ + 2

y = ⁷/₄x -¹³/₄

Question 15

Find the inverse of

y = 3x - 1

Answer 15

x = 3y - 1

3y = x + 1

y = (x + 1)/3