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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 _.