DECK 1: Introduction to the Cartesian Plane and Linear Ideas Flashcards
What is the slope of a line?
it is the steepness
How do a lot of people think about the slope (the slope)?
rise/run
or
change in y / change in x
what is the cartesian plane?
it is the thing we plot points on with the x y axis.. named after RENE DESCARTES, french philosopher and mathematician.
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?
1
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?
-1
If a slope of zero is 0 degrees, what is a slope of 1?
45 degrees uphill, a perfect diagonal
if a slope of zero is 0 degrees, what is a slope of -1?
45 degrees downhill (or -45 degrees)
What does “horizontal” mean?
left to right, like looking across the horizon
What does “vertical? mean?
up and down, like vertical columns holding up a building
What is a solution to an equation?
A solution is the set of values that makes an equation TRUE.
What does it mean to “satisfy” an equation?
It means you made the equation true. Solutions satisfy equations.
What are the slopes of the diagonals of a square?
+1 going up L to R, and -1 going down from L to ROW
How can you think of a slope of 1 or -1?
If you draw a square, think of the diagonals.. 45 degrees!
What is an interesting fact about slopes between -1 and +1?
HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1
What is the slope of a flat horizontal surface?
ZERO
What is the slope of a horizontal line?
ZERO
What is the slope of a vertical line?
undefined
what is the slope of a line that goes straight up and down?
undefined
the number 0/5 is equal to :
zero. 0
the number 5/0 is equal to :
undefined
Why can’t you divide by zero? (why can zero be in the top and not the bottom?)
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
What is the x intercept of a line? (what are the coordinates?)
Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )
What is the y intercept of a line? (what are the coordinates?)
Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )
what are the coordinates of a point?
(x,y), the x and y value.
What is the y coordinate for all x-intercepts?
zero. (x, 0), all x intercepts have a height of zero because they are on the x axis.
What is the x coordinate for all y-intercepts?
zero.(0, y) all y intercepts are in the middle, not left or right, because they are on the y axis.
what does the x coordinate tell you?
how far you go left (-) or right (+)
what does the y coordinate tell you?
how far you go up (+) or down (-)
How can you always get rid of fractions in any equation?
Multiply every term by the LCD (plop the LCD in the numerators, then simplify)
What is a solution to an equation?
the values that make the equation TRUE
If an x intercept is 455, what point is on the line?
(455, 0)
If a y intercept is 990, what point is on the line?
(0, 990)
what does a slope of zero look like?
horizontal, flat from left to right. The x axis has a slope of zero.
what does a slope that is undefined look like?
vertical, straight up and down. The y axis has a slope of zero.
what is the origin?
the point (0,0)
what is an undefined slope look like?
up and down (vert)
what does a zero slope look like?
left to right (horiz)
what is the point (0,0) called?
the origin
