DECK 2: ALGEBRA 1 TOPICS

Question 1

What is a solution to an equation?

Answer 1

A solution is the set of values that makes an equation TRUE.

Question 2

What does it mean to “satisfy” an equation?

Answer 2

Make the equation true.

Question 3

When you graph a line, what are you actually graphing?

Answer 3

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.

Question 4

When you graph a line, what is it?

Answer 4

It is a bunch of points!!! all have coordinates (x,y)

Question 5

How can you find the x intercepts from an equation of a line?

Answer 5

Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)

Question 6

How can you find the y intercepts from an equation of a line?

Answer 6

Plug zero in for X and solve for Y. The coordinates wll be (0, Y)

Question 7

What is the slope formula you use when trying to find the slope if you are given two points?

Answer 7

m = ( y - y ) / ( x - x )

Question 8

The three forms of equations of a line we use are :

Answer 8

point-slope form, slope-intercept form, general form

Question 9

Why is it called “point-slope” form?

Answer 9

There is a point and a slope explicitly shown in the form

Question 10

what is point-slope form a rearrangement of?

Answer 10

A rearrangement of the slope formula: y-y =m (x-x)

Question 11

What is the “point slope” form?

Answer 11

y-y = m (x-x)

Question 12

What is the slope-intercept form?

Answer 12

y = mx + b

Question 13

Why is it called “slope-intercept” form?

Answer 13

There is a slope and a slope explicitly shown in the formula

Question 14

What is the “standard” form?

Answer 14

ax + by = c no fractions or decimals and “a” is positive

Question 15

y=mx+b what form?

Answer 15

slope intercept

Question 16

y-y= m (x-x) what form?

Answer 16

point slope

Question 17

ax + by = c what form?

Answer 17

standard

Question 18

y = 1/2 x - 8 what form?

Answer 18

slope intercept

Question 19

y - 7 = 3 ( x + 9) what form?

Answer 19

point slope

Question 20

4x - 7y = 28 what form?

Answer 20

standard

Question 21

y = 1/2 x - 8 what is the slope?

Answer 21

1/2

Question 22

y - 7 = 3 ( x + 9) what is the slope?

Answer 22

3

Question 23

y = 1/2 x - 8 what point is given?

Answer 23

(0, -8) , the y intercept

Question 24

y - 7 = 3 ( x + 9) what point is given?

Answer 24

(-9, 7) it is in point slope form

Question 25

4x - 7y = 28 what is x intercept?

Answer 25

plug 0 in for y, 28/4=8, so (8,0)

Question 26

4x - 7y = 28 what is x intercept?

Answer 26

plug 0 in for x, 28/-7=-4, so (0,-4)

Question 27

parallel lines have ______

Answer 27

the same slope

Question 28

perpendicular lines have _____

Answer 28

opposite AND reciprocal slopes (switch sign and flip the fraction)

Question 29

How can you find the slope if it is in standard form?

Answer 29

Solve for y and change it into slope intercept form.

Question 30

How can you always get rid of fractions in any equation?

Answer 30

Multiply every term by the LCD (plop the LCD in the numerators, then simplify and all of the fractions VANISH!!!!)

Question 31

what is the “most popular” form?

Answer 31

slope intercept y=mx+b

Question 32

What is the graph of a line showing us?

Answer 32

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.

Question 33

If I take a point (x,y) that is on the line and plug it into the equation, what will happen?

Answer 33

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

Question 34

If I take a point (x,y) that is NOT on the line and plug it into the equation what will happen?

Answer 34

It will make a false statement (the sides won’t be equal). It will look like: 5=2 or 123 = -8

Question 35

If we are given an X, like x=5, and need to fine a Y that goes with it, how do we find it?

Answer 35

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.

Question 36

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?

Answer 36

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.

Question 37

when you see “ - y” or “ - x” what can you think of?

Answer 37

opposite of y and opposite of x

Question 38

If you are asked to find the equation passing through a given point with a given slope, what is the best form to use?

Answer 38

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])

Question 39

If you are given two points and need to find the equation of a line, how do you do it?

Answer 39

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.