DECK 2: Solutions, Equations and the Cartesian Plane

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

It means you made the equation true. Solutions satisfy equations.

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

what is the XY axis graph thing we plot lines and points on called?

Answer 4

the cartesian plane

Question 5

What is the cartesian plane?

Answer 5

That x y axis thing we draw and graph points on

Question 6

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

Answer 6

Multiply every term by the LCD (plop the LCD in the numerators, then simplify)

Question 7

What is the slope formula? (the slope formula?)

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

where does the point-slope form come from?

Answer 10

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

Question 11

Why is it called “slope-intercept” form?

Answer 11

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

Question 12

What is the slope-intercept form?

Answer 12

y = mx + b

Question 13

What is the “standard” form of a linear equation?

Answer 13

ax + by = c no fractions, a must be positive

Question 14

what is the “most popular” form?

Answer 14

slope intercept

Question 15

y = mx + b what form is this?

Answer 15

slope intercept

Question 16

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

Answer 16

point slope form

Question 17

Ax+By=C what form is this?

Answer 17

standard linear form

Question 18

If you graph a line, then any points, (x,y) on the line will make the equation ___ if you plug in the x and y

Answer 18

TRUE

Question 19

If you graph a line, then any points, (x,y) NOT on the line will make the equation ___ if you plug in the x and y

Answer 19

FALSE

Question 20

Solutions to equations are the values that make the equation ____

Answer 20

TRUE

Question 21

How can you tell if the point (5, -3) is a solution to a linear equation?

Answer 21

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.

Question 22

How can you tell if the point (5, -3) is on a line if you are given the equation?

Answer 22

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.

Question 23

What is the graph of a line showing us?

Answer 23

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 24

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 24

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 25

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 25

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 26

What is the x intercept of a line? (what are the coordinates?)

Answer 26

Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )

Question 27

What is the y intercept of a line? (what are the coordinates?)

Answer 27

Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )

Question 28

what are the coordinates of a point?

Answer 28

(x,y), the x and y value.

Question 29

What is the y coordinate for all x-intercepts?

Answer 29

zero. (x, 0), all x intercepts have a height of zero because they are on the x axis.

Question 30

What is the x coordinate for all y-intercepts?

Answer 30

zero.(0, y) all y intercepts are in the middle, not left or right, because they are on the y axis.

Question 31

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

Answer 31

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

Question 32

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

Answer 32

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

Question 33

What is the equation of the x axis?

Answer 33

y=0

Question 34

What is the equation of the y axis?

Answer 34

x=0

Question 35

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?

Answer 35

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.

Question 36

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?

Answer 36

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.

Question 37

How do you show that a point lies on a line?

Answer 37

Show that, when you plug the point in, you get a true mathematical statement.

Question 38

Describe what the line y=x looks line

Answer 38

positive diagonal line from bottom left to upper right, slope of 1, through the origin

Question 39

Describe what the line y=-x looks like

Answer 39

negative diagonal line from top left to bottom right, slope of -1, through the origin

Question 40

describe what the line y=12 looks like

Answer 40

horizontal, from left to right, through (0,12)

Question 41

describe what the line x=-8 looks like

Answer 41

vertical, straight up and down, through the point (-8,0) on the x axis. undefined slope

Question 42

If an x intercept is 455, what point is on the line?

Answer 42

(455, 0)

Question 43

If a y intercept is 990, what point is on the line?

Answer 43

(0, 990)