Flashcards in DECKS 1&2 COMBINED Deck (95)
What is a solution to an equation?
A solution is the set of values that makes an equation TRUE.
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.
What are the slopes of the diagonals of a square?
+1 going up L to R, and -1 going down from L to ROW
What is the equation of the y axis?
Describe what the line y=x looks line
positive diagonal line from bottom left to upper right, slope of 1, through the origin
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).
What is the slope formula you use when trying to find the slope if you are given two points?
m = ( y - y ) / ( x - x )
What is the slope of a vertical line?
when you see " - y" or " - x" what can you think of?
opposite of y and opposite of x
Parallel lines have ______ slopes, or slopes
y = 1/2 x - 8 what is the slope?
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 ___
parallel 2/3 and perp -3/2
y=mx+b what form?
what does a slope of zero look like?
horizontal, flat from left to right. The x axis has a slope of zero.
If you are given two points and need to find the equation of a line, how do you do it?
First, fine the slope using m=(y-y)/(x-x), then use that slope and EITHER OF THE POINTS. Put it in point slope form.
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 equation of the x axis?
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 )
How do a lot of people think about the slope (the slope)?
rise/run... or change in y / change in x
The three forms of equations of a line we use are :
point-slope, slope-intercept, standard
what is the origin?
the point (0,0)
perpendicular lines have _____
opposite AND reciprocal slopes
(switch sign and flip the fraction)
What do you know about all Y intercepts?
(0,y) they have an x coordinate of ZERO
Why is it called "slope-intercept" form?
There is a slope and an intercept explicitly shown in the formula
if a slope of zero is 0 degrees, what is a slope of -1?
-45 degrees downhill (traveling L to R)
How can you find the slope if it is in standard form?
Solve for y and change it into slope intercept form.
parallel lines have ______
the same slope
How can you find the x intercepts from an equation of a line?
Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)
What is the "point slope" form?
y-y = m (x-x) (has a point and a slope in it)