[M1 Math] Topic 7 The Coordinate Plane

Poll

Which do you like more?

• Engineers

• Astronauts

• Pilots

• Construction Workers

• Graphic Designers

• Navigators

• Fisherman

Careers

Used to determine a specific location in a large area.

Example: Let's find our location on the global map.

https://www.gps-coordinates.net/my-location

Mapping

Why is the Coordinate Plane Important?

The Coordinate Plane

The Coordinate Plane

​Unit 7 Lessons

1. What is a Coordinate Plane?

2. Graphing on the Coordinate Plane

3. Constant Rate of Change

4. Slope

The Coordinate Plane

1. What is a Coordinate Plane?

​Coordinate Plane

• A mathematical tool used to graph points, lines, and other objects.

• It is also known as a two-dimensional plane formed by the intersection of the Y and X axis.

Origin

• The point where the number lines intersect. (0, 0)

Coordinate

• A point on the coordinate plane, expressed in ordered pair (x,y) form. All points can be traced to an X and Y location.

Multiple Choice

The coordinates for the origin in the coordinate plane are________?

• (1,1)

• (0,0)

• (0,1)

• (1,0)

Multiple Choice

How do you correctly write an ordered pair?

• (y,x)

• (x,y)

• (0,0)

• (yy,x)

Multiple Choice

Which axis is the horizontal line?

• X axis

• Y axis

Multiple Choice

Which axis is the vertical line?

• X axis

• Y axis

The Coordinate Plane

What is a Coordinate Plane?

Quadrants

• Quadrant 1 located in the upper right of the plane, contains positive X and Y coordinates. Example: (2, 3)

• Quadrant 2 located in the upper left of the plane, contains a negative X and a positive Y coordinates. Example: (-2, 3)

• Quadrant 3 located in the lower left of the plane, contains negative X and Y coordinates. Example: (-2, -3)

• Quadrant 4 located in the lower right of the plane, contains a positive X and a negative Y coordinates. Example: (2, -3)

Multiple Choice

How many quadrants are there in a coordinate plane?

• 1

• 2

• 3

• 4

Multiple Choice

In which quadrant is the letter P?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

Where is point F located?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Multiple Choice

Where is point B located?

• Quadrant I

• Quadrant II

• Quadrant III

• None

Multiple Choice

Where is point C located?

• Quadrant I

• Quadrant II

• Quadrant III

• None

Multiple Choice

What is the order pair for D?

• (3,-5)

• (5,3)

• (-5,3)

• (-3,5)

Lesson 2: Graphing on the CP

"Graphing" is the method of drawing ordered pairs on a coordinate plane.

Graph (-2, 4)

• This point is in quadrant 2 of the coordinate plane.

Coordinate Plane

Multiple Choice

What is the ordered pair for C?

• (4,0)

• (0,4)

• (0,-4)

• (-4,0)

Multiple Choice

What is the ordered pair for E?

• (-3, 0)

• (0,-3)

• (0,3)

• (3,0)

Multiple Choice

What is the ordered pair for F?

• (-4,4)

• (4,4)

• (4, -4)

• (-4, -4)

Multiple Choice

What are the coordinates for the origin?

• (-1.5, -2.5)

• (-3, 1)

• (2, 3)

• (0, 0)

Multiple Choice

What is the coordinate of the red point?

• (-1.5, -2.5)

• (-3, 1)

• (2, 3)

• (0, 0)

Multiple Choice

Which coordinates belong in Quadrant 1?

• (-8, 1)

• (1, -8)

• (9, 5)

• (-5, -9)

Multiple Choice

Which coordinates belong in Quadrant 2?

• (-8, 1)

• (1, -8)

• (9, 5)

• (-5, -9)

Multiple Choice

Which coordinates belong in Quadrant 3?

• (-8, 1)

• (1, -8)

• (9, 5)

• (-5, -9)

What do you see when you look in the mirror???

Think of OPPOSITES.

Multiple Choice

Which set of ordered pairs are a reflection over the X axis?

• (2, -5) and (-2, 5)

• (3, 12) and (12, 3)

• (7, -4) and (7, 4)

• (10, 10) and (-10, -10)

Multiple Choice

Name the ordered that is a reflection of (4,-8) across the x-axis.

• (4, -8)

• (-4,8)

• (4,8)

• (-4,-8)

Multiple Choice

Name the ordered that is a reflection of (-2,8) across the y-axis.

• (-2, -8)

• (-2,8)

• (-2,-8)

• (2,8)

Multiple Choice

Name the ordered pair that is a reflection of (–3, 2) across the x-axis.

• (3, 2)

• (–3, –2)

• (3, –2)

• None of the choices

Multiple Choice

Name the ordered pair that is a reflection of

(2, –4) across the x-axis.

• (-2, 4)

• (-2, -4)

• (2, 4)

• None of the choices

Multiple Choice

Name the ordered pair that is a reflection of

(2, –4) across the x-axis.

• (-2, 4)

• (-2, -4)

• (2, 4)

• None of the choices

Lesson 3: Constant Rate of Change

Constant Rate of Change compares how two quantities change.

• Using a table or graph, you can calculate the constant rate of change.

• On a graph, X (output) remains constant, while the value of Y (input) increases.

Coordinate Plane

​When the value of X increases exponentially or at odd rates, it is not constant

​When the value of X increases at an equal rate, it is at a constant rate of change

​When the value of Y remains the same regardless of the change in X, there is no rate

Lesson 3: Constant Rate of Change

• X- Number of cars

• Y- Money ($)

• Y/X = constant rate of change (Unit Rate)

• 40/5 = $8 per car

Coordinate Plane

Multiple Choice

Which table below has a constant rate of change of 72?

Multiple Choice

Which one is my y values?

• Decorative Doughnuts

• Price

Multiple Choice

Marcus can download two songs from the internet each minute. This is shown in the table below. Find the rate of change.

• 4

• 3

• 1

• 2

Multiple Choice

What is the constant rate of change between the quantities in the table?

• $6.74 per hour

• $23.13 per hour

• $9.25 per hour

• $0.11 per hour

Multiple Choice

The graph represents the distance traveled while driving on a highway. Find the constant rate of change.

• 100 miles per hour

• 20 miles per hour

• 45 miles per hour

• 60 miles per hour

Multiple Choice

What is the rate of change for the following graph?

• 80

• 20

• 40

• 160

Multiple Choice

The table and the graph show the daily charge to rent a carpet cleaner for two different companies. Which company charges less per hour?

• Carpets Plus

• Sweepers R Us

• Both are the same

​​How to calculate Slope on a CP

Example 1

Lesson 4: Slope

Four Types of Slope

• Positive: up and to the right OR down and to the left

• Negative: up and to the left OR down and do the right

• Zero: no vertical change, horizontal line 

• Undefined: no horizontal change, vertical line

Multiple Choice

Identify the type of slope.

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

Identify the type of slope.

• Postive

• Negative

• Zero

• Undefined

Slope from Two Ordered Pairs

Multiple Choice

Find the slope of the line.

(5,2) (0,0)

• $$-\frac{2}{5}$$

• $$\frac{2}{5}$$

• $$-\frac{5}{2}$$

• $$\frac{5}{2}$$

Multiple Choice

Find the slope of the line that contains (3, -4) and (-1, 6)

• $$m\ =\ 1$$

• $$m=\frac{5}{2}$$

• $$m=-\frac{5}{2}$$

• $$m=-1$$

Multiple Choice

Find the rate of change between the points (-2 , 10) & (4 , 14)

• 2/3

• -2/3

• 3/2

• 2/1

Multiple Choice

Find the slope:

• $$\frac{3}{4}$$

• $$\frac{4}{3}$$

• $$\frac{1}{4}$$

• 3

Multiple Choice

Find the slope of the line.

• -5/4

• 5/4

• -4/5

• 4/5

Multiple Choice

Find the slope of the line.

(1,5) (2,8)

• $$\frac{1}{3}$$

• $$-\frac{1}{3}$$

• $$3$$

• -3