DECK 2: ALGEBRA 1 TOPICS Flashcards
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?
Make the equation true.
When you graph a line, what are you actually graphing?
THE SOLUTION! Those are all of the points that make the equation true. All of the points that “work”. If you put any other pionts, (x,y) into the equation, they wont work, You will get a false statement.
When you graph a line, what is it?
It is a bunch of points!!! all have coordinates (x,y)
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)
How can you find the y intercepts from an equation of a line?
Plug zero in for X and solve for Y. The coordinates wll be (0, Y)
What is the slope formula you use when trying to find the slope if you are given two points?
m = ( y - y ) / ( x - x )
The three forms of equations of a line we use are :
point-slope form, slope-intercept form, general form
Why is it called “point-slope” form?
There is a point and a slope explicitly shown in the form
what is point-slope form a rearrangement of?
A rearrangement of the slope formula: y-y =m (x-x)
What is the “point slope” form?
y-y = m (x-x)
What is the slope-intercept form?
y = mx + b
Why is it called “slope-intercept” form?
There is a slope and a slope explicitly shown in the formula
What is the “standard” form?
ax + by = c no fractions or decimals and “a” is positive
y=mx+b what form?
slope intercept
y-y= m (x-x) what form?
point slope
ax + by = c what form?
standard
y = 1/2 x - 8 what form?
slope intercept
y - 7 = 3 ( x + 9) what form?
point slope
4x - 7y = 28 what form?
standard
y = 1/2 x - 8 what is the slope?
1/2
y - 7 = 3 ( x + 9) what is the slope?
3
y = 1/2 x - 8 what point is given?
(0, -8) , the y intercept
y - 7 = 3 ( x + 9) what point is given?
(-9, 7) it is in point slope form
4x - 7y = 28 what is x intercept?
plug 0 in for y, 28/4=8, so (8,0)
4x - 7y = 28 what is x intercept?
plug 0 in for x, 28/-7=-4, so (0,-4)
parallel lines have ______
the same slope
perpendicular lines have _____
opposite AND reciprocal slopes (switch sign and flip the fraction)
How can you find the slope if it is in standard form?
Solve for y and change it into slope intercept form.
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 and all of the fractions VANISH!!!!)
what is the “most popular” form?
slope intercept y=mx+b
What is the graph of a line showing us?
It is showing us all of the points, (x,y), that make the equation true. Every dot on the graphed line will make the equation true, they all work.
If I take a point (x,y) that is on the line and plug it into the equation, what will happen?
It will make a true mathematical statement (the left and the right side will be equal). It will look like 6=6 or 0=0 or -1.8 = -1.8
If I take a point (x,y) that is NOT on the line and plug it into the equation what will happen?
It will make a false statement (the sides won’t be equal). It will look like: 5=2 or 123 = -8
If we are given an X, like x=5, and need to fine a Y that goes with it, how do we find it?
substitute the 5 in for the x in the eqution and solve for y, That y value goes with the 5. The point (5, y) will be on the line.
If we are given a Y value, like y=8, and need to find the x that goes with it, how do you do it?
substitute the 8 in for the y in the equation and solve for x. That x goes with the 8. the point (x, 8) will be on the line.
when you see “ - y” or “ - x” what can you think of?
opposite of y and opposite of x
If you are asked to find the equation passing through a given point with a given slope, what is the best form to use?
If you are given a point and a slope, use POINT SLOPE!! y-y=m(x-x) OR y [opp y] = slope (x [opp x])
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.
