DECK 3: Advanced Linear Concepts Flashcards
(86 cards)
How do you show that a point lies on a line?
Show that, when you plug coordinates in for x and y in the function, you get a true mathematical statement.
What happens if you plug the coordinates of point (x,y) that is NOT on the line in for x and y in a function?
It will make a FALSE statement
How do you know if a graph will go through the origin?
If you can plug in the coordinates (0,0) in for x and y and get a true statement.
What does it mean to “SOLVE” an equation?
Find values that make the equation true
The graph of an equation is the set of all of the points, (x,y) that _____
will make the equation true when plugged in
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 does 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
how can you think of the points on the line y=x to help you graph it?
the x and y are equal. 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 and y are opposites. so (2, -2) and (-2, 2) and (-107, 107).
How can you think of points on the line 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)