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A rectangular coordinate plane

is a 2-dimensional graphing system that allows you to specify the exact location of a point, lines, and plane figures.

the x axis, the y axis, and the origin.

The main part of the rectangular coordinate plane are

The x axis

Is horizontal, running straight left and right.

The y axis

Is vertical, or perpendicular to the x axis.

The origin

Is the point where the x and y axes meet.

a point

on a plane is located in terms of two numbers

the point's x-axis position and its y-axis position.

A point on a plane is located in terms of two numbers

ordered pair

A pair of numbers that can be used to locate a point on a coordinate plane.

Determine the coordinates for the point on this graph:

Step 1. Determine the x coordinate. It really doesn't matter whether you find the x- or y-coordinate first, as long as you show the final pair as (x, y) — x followed by y.

Using the Rectangular Coordinate Plane

This kind of graph is used for representing the position of points, lines, and plane figures. Points plotted on a

Plotting Lines on the Coordinate Plane

plot the two points and draw a straight line between them.

How to Plot a straight line between points

Step 1: Plot the first point. Step 2: Plot the second point. Step 2: Draw a straight line between the two points.

A horizontal line

is a straight line that lies parallel to the x axis on the coordinate plane. If the coordinate plane is set up in the customary fashion, horizontal lines on the plane run straight left and right.

A vertical line

is a straight line that lies parallel to the y axis on the coordinate plan. If the coordinate plane is set up in the customary fashion, vertical lines on the plane run straight up and down.

The intercepts of a line

are the two special points where the line crosses the x- and y-axes.

x-intercept

the point where the line crosses the x-axis

y-intercept

the point where the line crosses the y-axis

the ordered pair (0,y)

The y-intercept occurs where the line crosses the y-axis, so it is shown as

The x-coordinate is always zero

where the line crosses the x-axis

the ordered pair (x,0)

The x-intercept occurs where the line crosses the x-axis, so it is shown as

The y-coordinate is always zero

where the line crosses the y-axis

Determine the x- and y-intercepts for this line.

Step 1: Find the coordinate where the line crosses the x-axis Step 2: Find the coordinate where the line crosses the y-axis

Finding the Slopes of Lines

Slope = Change in y / Change in x

two points to define a line

Points are important parts of a line. It takes at least

the slope of the line

is like the "slant" or "steepness" of a line on the coordinate plane.

rises from left to right

A line with a positive slope

falls from left to right

A line with a negative slope

is a horizontal line

A line with zero slope

is a vertical line

A line with an infinite (undefined) slope

The slope of a line

is defined as the ratio of the change in the y distance to the corresponding change in the x distance.

Slope =

Change in y / Change in x

Slope is

Change in y divided by the change in x

m =

y2 - y1 / x2 - x1

m = y2 - y1 / x2 - x1

The slope of a line is defined as the ratio of the change in the y distance to the corresponding change in the x distance.

rises from left to right (uphill)

A line with a positive slope

rises from right to left (downhill)

A line with a negative slope

m = delta y / delta x

m = y2 - y1 / x2 - x1 is sometimes written as

So the slope of the line is 1.5.

For a certain line plotted on a coordinate plane, the slope increases upward 4 units in the y direction for every 3 in the positive-x direction. What is the slope of the line.

The slope of a line is defined as

the ratio of the change in the y distance to the corresponding change in the x distance.

quadrant 2

which quadrant is (-4,3) in?

Quadrant 1

The upper right quadrant on the cartesian plane

quadrant 3

which quadrant is (-4,-3) in?

Quadrant 4

The lower right quadrant on the cartesian plane

origin

The centre point of a number line (ground floor of a hotel, freezing point on a thermometer)

x axis

The horizontal axis on a coordinate graph, for the varaible that controls the other (an axis ia a line on a graph)

y axis

has the dependent variable, the vertical line on a graph

Transformation

a movement on the cartesian plane

reflection

It is a transformation that flips a figure over a line of reflection.

rotation

It is a transformation that turns a figure about a fixed point.

translation

It is a transformation that moves points the distance and in the same direction.

object

the original shape

image

the resulting figure AFTER a transformation is performed on it

A' (A prime)

If point A is moved on the cartesian plane, what is the new point called?

coordinate plane

A plan formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.

axes

the two real number lines that form the coordinate plane

x-axis

The horizontal axis on a coordinate plane.

y-axis

The vertical axis on a coordinate plane.

quadrant

the x- and y-axes divide the coordinate plan into four regions. each region is called a ________________.

x-Coordinate

is the first number in an ordered pair and it represents the location relative to the x-axis.

y-Coordinate

The vertical measure, which is the second number in an ordered pair.

plotting the point

locating a point in the coordinate plane that corresponds to an order pair

Solution

The value or values that make an equation or inequality true.

liner equation

an equation variables whose graph is a straight line

Table of values

a table that contains several ordered pairs that make an equation in two variables true

graph of a linear equation

In x and y, is the set of all points (x,y) that are solutions of a

vertical line

Straight up and down line (height)

horizontal line

Slope of zero

slope from a graph

the ratio of the line's rise to the run

slope from two points

the ratio of the difference in y-coordinates to the difference in the x-coordinates for any two points on the graph of a linar equation

Relation

A Smart Art graphic type that compares connections between concepts.

Domain

The ______________________ is all the possible INPUT, X, values.

Range

The difference between the greatest number and the least number in a set of data.

function

If you repeat an INPUT, and you always get the same OUTPUT, your data is a ______________________ .

vertical-line test

The test that visually determines whether or not a relation is a function or not.

Linear Equation

A polynomial equation of the first degree whose graph is a line.

slope

(y₂-y₁)/(x₂-x₁)

tilt of a line

A ration that describes the

Slope-Intercept Form

a linear equation written in the form y = mx + b, where m represents slope and b represents the y-intercept

Function notation

In general, a special numerical relationship where the symbol f(x) replaces y and is read as "the value of f at x" or simply as "f of x".

function rule

An equation that describes a function.

Scatter plot

is a graph used to determine whether there is a relationship between paired data. Scatter plots can show trends in data.

positive correlation

y tends to increase, as x increases

negative correlation

y tends to decrease, as x increases

no correlation

The values show no relationship.

trend line

A line that closely fits the data points in the scatter plot.

system of linear equations

What two or more linear equations form.

solution of the system

Any ordered pair that is a solution of each equation in the system is a _.

linear equality

When you replace the equal sign in a linear equation with >, <, ≥, or ≤, the result is this.

system of linear inequalities

Two ore more linear inequalities together.

solution of a system of linear inequalities

Any ordered pair that makes each inequality in the system true is a _.