DECK 1: Introduction to the Cartesian Plane and Linear Ideas

Question 1

What is the slope of a line?

Answer 1

it is the steepness

Question 2

How do a lot of people think about the slope (the slope)?

Answer 2

rise/run

or

change in y / change in x

Question 3

what is the cartesian plane?

Answer 3

it is the thing we plot points on with the x y axis.. named after RENE DESCARTES, french philosopher and mathematician.

Question 4

If you draw a square with the diagonals as an X, what is the slope of the diagonal that goes from bottom left to upper right corner?

Answer 4

1

Question 5

If you draw a square with the diagonals as an X, what is the slope of the diagonal that goes from top left to the bottom right corner?

Answer 5

-1

Question 6

If a slope of zero is 0 degrees, what is a slope of 1?

Answer 6

45 degrees uphill, a perfect diagonal

Question 7

if a slope of zero is 0 degrees, what is a slope of -1?

Answer 7

45 degrees downhill (or -45 degrees)

Question 8

What does “horizontal” mean?

Answer 8

left to right, like looking across the horizon

Question 9

What does “vertical? mean?

Answer 9

up and down, like vertical columns holding up a building

Question 10

What is a solution to an equation?

Answer 10

A solution is the set of values that makes an equation TRUE.

Question 11

What does it mean to “satisfy” an equation?

Answer 11

It means you made the equation true. Solutions satisfy equations.

Question 12

What are the slopes of the diagonals of a square?

Answer 12

+1 going up L to R, and -1 going down from L to ROW

Question 13

How can you think of a slope of 1 or -1?

Answer 13

If you draw a square, think of the diagonals.. 45 degrees!

Question 14

What is an interesting fact about slopes between -1 and +1?

Answer 14

HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1

Question 15

What is the slope of a flat horizontal surface?

Answer 15

ZERO

Question 16

What is the slope of a horizontal line?

Answer 16

ZERO

Question 17

What is the slope of a vertical line?

Answer 17

undefined

Question 18

what is the slope of a line that goes straight up and down?

Answer 18

undefined

Question 19

the number 0/5 is equal to :

Answer 19

zero. 0

Question 20

the number 5/0 is equal to :

Answer 20

undefined

Question 21

Why can’t you divide by zero? (why can zero be in the top and not the bottom?)

Answer 21

10/2 asks “how many times do you add 2 to itself to get to 10?” the answer is 5.

10/0 asks “how many times do you add 0 to itself to get to 10?” the answer is there is no answer. undefined

Question 22

What is the x intercept of a line? (what are the coordinates?)

Answer 22

Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )

Question 23

What is the y intercept of a line? (what are the coordinates?)

Answer 23

Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )

Question 24

what are the coordinates of a point?

Answer 24

(x,y), the x and y value.

Question 25

What is the y coordinate for all x-intercepts?

Answer 25

zero. (x, 0), all x intercepts have a height of zero because they are on the x axis.

Question 26

What is the x coordinate for all y-intercepts?

Answer 26

zero.(0, y) all y intercepts are in the middle, not left or right, because they are on the y axis.

Question 27

what does the x coordinate tell you?

Answer 27

how far you go left (-) or right (+)

Question 28

what does the y coordinate tell you?

Answer 28

how far you go up (+) or down (-)

Question 29

How can you always get rid of fractions in any equation?

Answer 29

Multiply every term by the LCD (plop the LCD in the numerators, then simplify)

Question 30

What is a solution to an equation?

Answer 30

the values that make the equation TRUE

Question 31

If an x intercept is 455, what point is on the line?

Answer 31

(455, 0)

Question 32

If a y intercept is 990, what point is on the line?

Answer 32

(0, 990)

Question 33

what does a slope of zero look like?

Answer 33

horizontal, flat from left to right. The x axis has a slope of zero.

Question 34

what does a slope that is undefined look like?

Answer 34

vertical, straight up and down. The y axis has a slope of zero.

Question 35

what is the origin?

Answer 35

the point (0,0)

Question 36

what is an undefined slope look like?

Answer 36

up and down (vert)

Question 37

what does a zero slope look like?

Answer 37

left to right (horiz)

Question 38

what is the point (0,0) called?

Answer 38

the origin