DECK 1: ALGEBRA 1 TOPICS Flashcards
What is your favorite class?
ALGEBRA 2
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 (traveling L to R)
if a slope of zero is 0 degrees, what is a slope of -1?
45 degrees downhill (traveling L to R)
What does “horizontal” mean?
left to right.. like a floor or table top
What does “vertical? mean?
up and down
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 (and they are perpendicular)
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 istelf 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. 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. all y intercepts are in the middle, not left or right, because they are on the y axis.
What do you know about all X-intercepts?
(x,0) they have a y coordinate of ZERO
What do you know about all Y intercepts?
(0,y) they have an x coordninate of ZERO
Parallel lines have ______ slopes, or slopes
the same
Perpendicular lines have _____ slopes, or slopes
OPPOSITE SIGN AND RECIPROCAL
If a line as a slope of 2/3, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___
2/3 and perp -3/2
If a line as a slope of -5, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___
-5 and perp 1/5
How can you tell if the point (5, -3) is a solution to a linear equation?
If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.
How can you tell if the point (5, -3) is on a line if you are given the equation?
If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.
What is the equation of the x axis?
y=0
What is the equation of the y axis?
x=0
What is the equation of a vertical line that goes through the x axis at 7? How can you think of that line to help make sense of it?
x = 7. You can think “all of the points on this line have an x value of 7, so you are a solution as long as your x=7.
What is the eqution of a horizontal line that goes througyh the y axis at 8? How can you think about it to help you?
y = 8. Since y is the height, you can think of it as all of the points that have a height of 8. Also, you can think of it as all of the points that have a y value of 8, so you are a solution if your y value is 8.
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)
How do you show that a point lies on a line?
Show that, when you plug the point in, you get a true mathematical statement.
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.
how can you think of the points on the line y=x to help you graph it?
all of the x values are equal to all of the y values.. so (2,2), (3,3), (5,5), (-100,-100) are all in the solution set and on the line
How can you think of the points on the line y=-x to help you graph it?
the x values are opposite the y values… so (2, -2) and (-2, 2) and (-107, 107).
How can you think of points on the lone y=5 to help you graph it?
all of the points on the cartesian plane with a y value of 5… (2,5), (9,5), (-200,5)
How can you think of the line x=6 to help you graph it?
all of the points on the cartesian plane with an x value of 6: (6, 0), (6, -3), (6, 24.3), (6, -2000)
Describe what the line y=x looks line
positive diagonal line from bottom left to upper right, slope of 1, through the origin
Describe what the line y=-x looks like
negative diagonal line from top left to bottom right, slope of -1, through the origin
describe what the line y=12 looks like
horizontal, from left to right, through (0,12)
describe what the line x=-8 looks like
vertical, straight up and down, through the point (-8,0) on the x axis. undefined slope
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
what is the XY axis graph thing we plot lines and points on called?
the cartesian plane
