8. Graphing Coordinates and Lines

Practice: Labeling Coordinates What are the coordinates of the red dot?

(-8,-1) Because the red dot is... 8 spaces to the LEFT of 0 and 1 space DOWN from 0.

Practice: Labeling Coordinates What are the coordinates of the green dot?

(3,7) Because the green dot is... 3 spaces to the RIGHT of 0 and 7 spaces UP from 0.

Practice: Labeling Coordinates What are the coordinates of the blue dot?

(7,-7) Because the blue dot is... 7 spaces to the RIGHT of 0 and 7 spaces DOWN from 0.

How do we graph a line using y=mx+b?

1. Find 3 solution pairs. 2. Graph them on the coordinate plane. 3. Connect the dots to make the line.

How do we find a solution pair using y=mx+b?

1. Plug in any number for x. 2. Solve for y. 3. Your solution pair will be (x,y)

How to Label Coordinates

Every point on the graph has an x-coordinate and y-coordinate. Coordinates are written between parentheses. The x is always first and the y is second. (x,y) If the point is to the RIGHT of 0, the x coordinate will be POSITIVE. If the point is to the LEFT of 0, the x coordinate will be NEGATIVE. If the point is UP from 0, the y coordinate will be POSITIVE. If the point is DOWN from 0, the y coordinate will be NEGATIVE.

Example: Labeling Coordinates Label the coordinate on the graph.

The coordinates of the green point are (4,6) The 4 tells us how many spaces to the right it is from 0. The 6 tells us how many spaces up it is from 0.

What is the origin?

The origin is the point (0,0). It is where the x-axis and y-axis meet.

What is the x-axis?

The x-axis is the horizontal line on the coordinate plane. It is where y = 0.

What is the y-axis?

The y-axis is the vertical line on the coordinate plane. It is where x = 0.

What is the coordinate plane?

This picture shows the coordinate plane. It is where you graph lines.

Practice: Finding a solution pair. y = x+2

y = x+2 1. Plug in any number for x. Let's plug in 4. 2. y = 4+2 = 6 3. Your solution pair is (4,6) which is a point on the line.

Practice: Graphing a Line y = 3x+1

y = 3x+1 1. Pick in 3 different numbers for x and solve for y. y = 3(-3)+1 = -8 y = 3(0) +1 = 1 y = 3(3) + 1 = 10 So, your solution pairs are... (-3,-8) (0,1) (3,10) 2. Graph the 3 points on the coordinate plane. 3. Connect the dots to make the line.

What is the linear equation? What are the variables?

y = mx + b This equation can help us graph a line. This equation has two variables: x and y. It has two constants, m and b. m describes the slope or tilt of the line. b tells us where the line crosses the y-axis. It's also called the y-intercept.