# Meet Slope

- Author:
- Jakob Swanson, Tim Brzezinski

## SOME SIMPLE INSTRUCTIONS

__independently__. 2. There are 5 questions that I will collect answers from these questions that are labeled with a ****. You will write these answers on a separate sheet of paper with your name on it and I will collect it. These will be at different points in the class and not all at once. Some of your responses will be celebrated by me writing it on the board but it will remain anonymous. 3. If there are any questions that you would rather write or draw on a separate sheet of paper, that is fine. I will come around to check your work.

## Learning Objectives (Today we will...)

## Math Objective

*m*is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation

*y=mx*for a line through the origin and the equation

*y=mx+b*for a line intercepting the vertical axis at b.

## A Quick Review

Which is the best representation of a quotient?

What do we call lines that do not intersect?

## How do you know?

****Out of the 3 rollercoasters that I drew below which of them is the steepest? How do you know?

## How do we determine slope?

****How does this program know what the slope of the ramp is?

What does it mean when the slope of the ramp =0?

What does it mean for the slope to be UNDEFINED!

## What would the slope of this ride be and why?

Is the slope a quotient?

****Explain your previous answer.

## Lines with the same slope

****As you play around with the slope of the two lines, what happens when you set the slopes equal to each other?

## Another Quick Review

How can I show two triangles are similar? Select all that apply.

## Slope Triangles

Is Triangle 1 a slope triangle?

Is Triangle 2 a slope triangle?

Why is Triangle 3 a slope triangle?

What is similar between Triangle 1,2 and 3? Select all that apply.

## I claim that all 4 triangles in this activity are similar.

****How would you defend this argument?

## Extended Questions

Rewrite the following in your own words.
*Comprehend the term “slope” to mean the quotient of the vertical distance and the horizontal distance between any two points on a line.*

Your skateboarding down a hill, you're going pretty fast and you estimate the slope of the hill to be around -5. Your friend is skating right next to you and claims his hill has a slope is -6. Is this possible if you are on the same hill? Justify your answer using the idea of parallel lines.

Using what you know about slope, which rollercoaster from the drawings was the steepest?