The Adventures of Lady Point

Try some more! What is the slope of her new path below? What is the slope of the line between Mr. Bumbline Bee at point (-3, -4) to Lady Point at point (2, -4)?

Slope = (-4- -4)/(-3- 2) = (-4+4)/(-5) = 0/-5 = 0

So, Lady Point's path here had a slope of 1! For every space she moved to the right, she also moved up one block, until she hit (3, 3).

Thanks for the help Mr. Bumbline Bee! But what about the slope of my path?

Slope is the change y-coordinate (up/down) divided by the change in the x-coordinate (left/right). The formula is (y1-y2)/(x1-x2).

So with Lady Point's path here, she traveled up 3 blocks and to the right 3 blocks. Thus, her change in the y-coordinate was positive 3, and the change in the x-coordinate was positive 3. 

Slope Formula: (y1-y2)/(x1-x2) (0-+3)/(0-+3) -3/-3 1

That's right! Lady Point is now at (3, 3). So how far did she travel left/right and how far did she travel up/down?

Try some more! What is the slope of her new path below? What is the slope of the line between Mr. Bumbline Bee at point (-5, 1) to Lady Point at point (-3, -4)?

Slope = (1- -4)/(-5- -3) = (1+4)/(-5+3) = 5/-2

We can mark how many spots she moved left/right and up/down by drawing and counting the number of spaces on the coordinate plane. Remember that Lady Point started her journey at the origin (0, 0) with Mr. Bumbline Bee. Thus, we start counting spots from that starting point.

She would move from point to point discovering new coordinates of the land. She would go up and down with the y-axis and she would turn left and right on the x-axis.

There once was a ladybug named Lady Point. She likes to travel through all around outside. She just travels alone, though. 

Lady Point loves her traveling! There she goes again! What point on the coordinate plane did she travel to now? And how far left/right and up/down did she travel from where she started at Mr. Bumbline Bee?

Mr. Bumbline Bee follows her to (3, 3) traveling at a slope of 1. Now, (3, 3) is the new starting point for Lady Point's next journey. 

They both start at the origin of the coordinate plan. This starting point has an x value of 0, meaning that the point has not moved left or right at all. It also has a y value of 0 meaning that the point has not moved up or down at all. The origin is (0, 0).

Lady Point was so happy that she found a friend to help her! They began tracking their journeys on the coordinate planes. Which axis goes up and down? Which axis goes left/right?

Therefore, Lady Point moved 8 blocks to the LEFT and 2 blocks DOWN. When we move to the left or when we move down, the number becomes NEGATIVE. When we move to the right or when we move up, the number stays POSITIVE. Let's find the slope of her path.

The slope of the line between (3, 3) and (-5, 1) is:

So, the slope of her second path is 1/4 !

Lady Point begins her journey, but Mr. Bumbline Bee stays at the origin so that they can see how far she traveled. 

What point on the coordinate plane is Lady Point standing at now?

Lady Point was very interested to see how far she had traveled one day. She wanted to know how far she went up or down and how far she went left or right.

However, each time she moved she couldn't remember her starting point. She needed a friend to help her trace her steps! But poor Lady Point was all alone. 

No problem Lady Point! Next time I'll do the leading!

Whew! That was a lot of flying around! Thank you for all your help Mr. Bumbline Bee.&#160;

Remember! Slope is the change y-coordinate (up/down) divided by the change in the x-coordinate (left/right). The slope formula is (y1-y2)/(x1-x2).

The Adventures of Lady Point

Finding the slope of a line given 2 points on a coordinate plane.

All of a sudden, Mr. Bumbline Bee shows up!

Hi there Lady Point! Bzzz I can help you!

She moved to the LEFT 8 spaces and DOWN 2 spaces. Now, she is at point (-5, 1). But, she started at (3, 3). What is the slope formula?