Cartesian Plane and Slope

RECTANGULAR COORDINATE SYSTEM and SLOPE

by Ricky Negapatan

​OUR TARGET FOR TODAY

​- Name the points in the cartesian plane

​- Identify the quadrant of the coordinates

- Identifying slope (direction)

- Finding slope of a line (steepness)

- Slope from a Table

- Slope from an Equation- Identifying slope (direction)

​THE COORDINATE PLANE

​ The coordinate plane is a two-dimension plane that is formed when the x-axis (running horizontally - left/right) intersects with the y-axis (running vertically - up/down).

​THE ORIGIN

​The x-axis and y-axis intersect at a point called the ORIGIN.

​

Each point on the coordinate plane can be represented by an ordered pair (x,y) which state the coordinate location of each point.

​

The origin is located at (0,0).

THE QUADRANTS

This intersection also creates four quadrants where points can be plotted.

​

To name quadrants, begin at the top right where all the positive values of both x and y are located.

This is Quadrant I.

To name the others, move in a counterclockwise rotation.

Multiple Choice

In which quadrant is letter N?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

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

The point (-2, -3) is in which quadrant?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

PLOTTING POINTS

Although there are two coordinates given for an ordered pair, it is a series of these two movements that result in one plotted point.

First follow the x to move left/right,

then follow the y to move up/down.

​Plot and label the coordinates on a cartesian plane

A ( 5, 4 ) ,

B ( -3, 0 ) ,

C ( -1, -2 )

Fill in the Blanks

What is the coordinate for C?

Fill in the Blanks

What is the coordinate for A?

Fill in the Blanks

What is the coordinate for D?

​SLOPE

• ​the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Multiple Choice

What type of slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What type of slope?

• Positive

• Negative

• Zero

• Undefined

Multiple Choice

What type of slope?

• Positive

• Negative

• Zero

• Undefined

Finding the Slope of a Line

Slope can tell us how steep a line is!

​

Each line can be assigned a value that tells us how steep the line is.

​

Slope is written as a ratio (rise/run)

​

Always make sure to simplify your answer!

Multiple Choice

Find the slope of the line below using rise/run.

• $$\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$3$$  

• $$\frac{1}{3}$$  

Finding the Slope From a Table

• Slope = change in y/change in x

• Use the table to find the value the y is changing by. That is the numerator!

• Use the table to find the value the x is changing by. That is the denominator!

• ANOTHER OPTION: Graph the points and count rise/run

Multiple Choice

Find the slope. Simplify, if you can.

• $$\frac{2}{5}$$  

• $$-\frac{2}{5}$$  

• $$\frac{5}{2}$$  

• $$2$$  

Finding the Slope From an Equation

Fill in the Blanks

Identify the slope in the equation: $y=x+5$  

Fill in the Blanks

What is the slope of the line with the equation  $y=4x+12\ ?$  

Fill in the Blanks

What is the slope of the line with the equation  $y=\frac{2}{3}x+6\ ?$  

Finding the Slope of Two Points

Finding the Slope of Two Points

Fill in the Blanks

What is the slope of (-5,-4) and (5,1)?

​BE A SLOPE ENGINEER!!!