Math - Graphing And Linear Equations

Front 1

In the rectangular coordinate system: The horizontal line is called the:
The vertical line is called the:

Back 1

The horizontal line is called the: x - axis
The vertical line is called the: y - axis

Front 2

What are the names for the quadrants in the rectangular coordinate system?

Back 2

starting with the upper right quadrant and moving counter-clockwise:
-first quadrant
-second quadrant
-third quadrant
-fourth quadrant

Front 3

The pair of numbers arranged in the order (x,y), which represent the x-values and y-values, are called:

Back 3

an ordered pair

Front 4

The x-value is called the:
The y-value is called the:

Back 4

The x-value is called the: x-coordinate or abscissa.
The y-value is called the: y-coordinate or the ordinate.

Front 5

If a point is designated a label, say A, then as a matter of notation, that label may appear:

Back 5

in front of the coordinates, eg. if point A has coordinates (5,6), one may write: A(5,6).

Front 6

An equation with two variables is called a linear equation if:

Back 6

the exponent of each variable is 1.

Front 7

What does a linear equation look like when graphed on the x - y plane?

Back 7

a straight line, hence the name.

Front 8

What is the process for graphing a linear equation?

Back 8

1) Make two columns with x on one side and the equation where y is isolated on the other.
2) Place arbitrary values for x under the x column and substitute these values for x in the equation.
3) The result will be the value of y. Place this value under the y column.
4) Repeat for each arbitrary value.

Front 9

The steepness of a linear equation is called the:

Back 9

slope

Front 10

The slope is measured by:

Back 10

the ratio of the Rise and the Run. ie. Rise / Run

Front 11

The Rise is:

Back 11

The Rise is the vertical difference between two points on the line. ie. Rise = y₂ - y₁

Front 12

The Run is:

Back 12

The Run is the horizontal difference between two points on the line. ie. Run = x₂ - x₁

Front 13

The Slope Formula:

Back 13

m = y₂ - y₁ / x₂ - x₁
Where m is used to designate the slope.

Front 14

The Slope of a line is ascending if:
The Slope of a line is descending if:

Back 14

The Slope of a line is ascending if: it is going up from left to right. (the slope is positive)
The Slope of a line is descending if: it is falling from left to right. (the slope is negative)

Front 15

If a Slope is "undefined," it means:

Back 15

that there is no slope. It will also be vertical. Vertical lines do not have slopes.

Front 16

All Horizontal lines have a slope of:

Back 16

zero

Front 17

What are the four different types of slopes?

Back 17

1) Positive slope: Line is ascending from left to right.
2) Negative slope: Line is descending from left to right.
3) No slope or "Undefined" slope: Line is vertical.
4) Zero slope: Line is horizontal.

Front 18

What is the point-slope formula?

Back 18

y - y₁ = m(x - x₁)

Front 19

When is the point-slope formula used?

Back 19

When we want to find the equation of a line when a point on that line and the slope are given.

Front 20

In a linear equation, if the equation is expressed as y in terms of x ie:
y = 2x + 5 then the coefficient of x is always equal to:

Back 20

the value of the slope.

Front 21

In a linear equation, if the equation is expressed as y in terms of x ie:
y = 2x + 5 and we substitute 0 for x, then the value of y is always equal to:

Back 21

the constant term of the final equation ie. 5 in this equation. (if we substitute 0 for x, the constant is also the y-intercept)

Front 22

If, in an ordered pair, x = 0 then the point is on the ___ axis.
This point is called:

Back 22

y axis;
This point is called the y-intercept.

Front 23

If, in an ordered pair, y = 0 then the point is on the ___ axis.
This point is called

Back 23

x axis;
This point is called the x-intercept.

Front 24

What is the slope-intercept formula?
What formula is it a variation of?

Back 24

y = mx + b; where b = y-intercept.

It is a variation of the point-slope formula.

Front 25

In the x-intercept, y =

Back 25

zero

Front 26

In the y-intercept, x =

Back 26

zero

Front 27

How do you find the x-intercept?

Back 27

Let y = 0 in the given equation and solve for x.

Front 28

How do you find the y-intercept?

Back 28

Let x = 0 in the given equation and solve for y.

Front 29

Vertical line formula:

Back 29

x = x₁

Front 30

Horizontal line formula:

Back 30

y = y₁

Front 31

Why is it very necessary to know the Vertical Line formula when trying to find the equation of a vertical line?

Back 31

Because vertical lines have a slope that is undefined. ie. zero as a denominator.

Front 32

How do you find the equation of a line if given two ordered pairs?

Back 32

1) Use the Slope formula to find the slope.
2) Use the Point-Slope formula to find the equation.

Front 33

If all the ordered pairs in a line have the same x value then:

Back 33

the line is a vertical line.

Front 34

If all the ordered pairs in a line have the same y value then:

Back 34

the line is a horizontal line.

Front 35

What are the steps in order to graph an inequality in two variables?

Back 35

1) Replace the inequality with an "equals sign."
2) Solve for y, then graph the resulting equation.
3) If the original inequality includes "equal to" as well, ie. ≤ or ≥ then the graph is included in the solution. If the original inequality does not include an "equal," then a shaded line should be used to indicate that the graph is not part of the solution.
4) The graph obtained divides the plane into two regions called "half-planes." Pick two values that makes a point in one of the planes. Substitute these values into the original inequality. If it is true, then shade the plane on that side of the line.