The Coordinate Plane

Welcome to the Spring Semester 2022

Welcome back

How are we going to work this second semester.

GED/HISET differences.​

Textbook for Math​

Some text here about the topic of discussion

The Coordinate Plane

By Luis Bello

Learning Outcomes

• Plot Ordered Pairs

  • Identify the components of the coordinate plane

  • Plot ordered pairs on the coordinate plane

• Identify Quadrants on the Coordinate Plane

  • Identify the four quadrants of a coordinate plane

  • Given an ordered pair, determine its quadrant

Some text here about the topic of discussion

The coordinate plane

The coordinate plane was developed centuries ago (in 1637, to be exact) and refined by the French mathematician René Descartes. In his honor, the system is sometimes called the Cartesian coordinate system. The coordinate plane can be used to plot points and graph lines. This system allows us to describe algebraic relationships in a visual sense, and also helps us create and interpret algebraic concepts.

The Components of the Coordinate Plane

The Components of the Coordinate Plane: The horizontal axis in the coordinate plane is called the x-axis. The vertical axis is called the y-axis. The point at which the two axes intersect is called the origin. The origin is at 0 on the x-axis and 0 on the y-axis.

To identify the location of this point, start at the origin (0, 0) and move right along the x-axis until you are under the point.

Look at the label on the x-axis.

The 4 indicates that, from the origin, you have traveled four units to the right along the x-axis.

This is the x-coordinate, the first number in the ordered pair.

From 4 on the x-axis move up to the point and notice the number with which it aligns on the y-axis. The 3 indicates that, after leaving the x-axis, you traveled 3 units up in the vertical direction, the direction of the y-axis.

This number is the y-coordinate, the second number in the ordered pair. With an x-coordinate of 4 and a y-coordinate of 3, you have the ordered pair (4, 3).

Plot the point (1, 3).

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Plot the point (−4,−2).​

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In which quadrant is the point (−7,10) located?​

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In which quadrant is the point (−10,−5) located?​

Multiple Choice

Which quadrant contains the point named by (2, 5)?

• Quadrant I
• Quadrant II
• Quadrant III
• Quadrant IV

Multiple Choice

In which quadrant is the following point?
(-3, 12)

• Quadrant I
• Quadrant II
• Quadrant III
• Quadrant IV

Multiple Choice

Which letter matches the coordinate (4, -6)?

• G
• Z
• K
• None of the above

Multiple Choice

What error did the student make when plotting the point (3, 4) according to the picture?                                                                                                                                                                                                                                                                                                                                                                         

• The student moved left along the x-axis when he should have moved right
• The student plotted the y-coordinate in place of the x-coordinate
• The student didn't make a mistake
• Both Options 1 and 2

Multiple Choice

If you were to plot the point (4, -12) what would be the correct method?

• Up 4, left 12
• Right 4, up 12
• Down 4, left 12
• Right 4, down 12

Multiple Choice

Where is point E located?

• ( 2, 0 )
• ( 2 , 2 )
• ( 0 , 2 )
• ( 0 , 0 )

Multiple Choice

The coordinate plane is divided by a horizontal number line called what? 

• y-axis
• origin
• x-axis
• quadrant

Multiple Choice

The axes divide the coordinate plane into four sections called what? 

• ordered pairs
• origins
• quadrants
• coordinate plane

Multiple Choice

The vertical number line in the coordinate plane is called what? 

• y-axis
• origin
• quadrant
• x-axis

Multiple Choice

When plotting points in a coordinate plane, which directions should you go first? 

• left or right
• up or down
• left
• up

Graphing Linear Equations

Learning Outcomes

• Graph an Equation Using Ordered Pairs

  • Create a table of ordered pairs from a two-variable linear equation

  • Graph a two-variable linear equation using a table of ordered pairs

  • Determine whether an ordered pair is a solution of an equation

• Graph Linear Equations in Different Forms

  • Solve for

  • Graph horizontal and vertical lines

• Graph an Equation Using Intercepts

  • Recognize when an ordered pair is a

  • Graph a linear equation using X and Y intercepts.

Multiple Choice

The point where the line crosses the y-axis is called the:

• origin
• x-intercept
• y-intercept
• slope

Multiple Choice

Which graph represents the table?

Multiple Choice

Which graph represents the equation $$y=4x-1$$  

Multiple Choice

Which ordered pair could represent a y-intercept on a graph?

• (6, 0)
• (0, 4)
• (-1, 3)
• (2, 0)

Multiple Choice

What error did the student make when plotting the point (3, 4) according to the picture?                                                                                                                                                                                                                                                                                                                                                                         

• The student moved left along the x-axis when he should have moved right
• The student plotted the y-coordinate in place of the x-coordinate
• The student didn't make a mistake
• Both Options 1 and 2

Multiple Choice

Which line is being represented by the graph?

• y = 3/4 X -3
• y = -3/4x + 4
• y = 3/4x + 4
• y = -3/4 x - 3

Multiple Choice

Find the slope.

• 3/2
• -3/2
• (-0,-3)
• none of the above

Multiple Choice

Find the slope of the line that passes through the points (2, 4) and (6, 12)

• 1/2
• -1/2
• 2
• -2

Multiple Choice

In the equation, y = mx + b, the letter b is the ___________.

• y-intercept
• x-intercept
• slope
• rate of change

Multiple Choice

Consider the equation:
y=-x+4
Identify the slope and y-intercept.

• m=4, b=-x
• m=-x, b=4
• m=1, b=4
• m=-1, b=4

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• x-intercept

Multiple Choice

Give the equation for the graph

• y = 5x - 3
• y = 4x + 2
• y =-2x + 5
• y = - 2x + 4