# 5.2: Math Man on the Slopes

*This activity is intended to supplement Algebra I, Chapter 4, Lesson 4.*

## Problem 1- Visually estimating slopes

Press **APPS** and select Cabri Jr. Open the file **MATHMAN**.

Math Man is cross-country skiing from left to right.

- Which part(s) of the hill has the best “ski slope” for Math Man? Explain.

Now open the file **DIPPER**. You will see a representation of the “Big Dipper”, a formation commonly recognized in the night sky.

The slopes of the lines of the segments are:

- Each segment is labeled with a letter. Match the slope with the segment. Record your answers below.
- How did you determine which slope belonged with which segment?

**Self-Check Point**

- I already know about and what each letter means. True False

## Problem 2 – Exploring precise slope

Open the file **SLOPE**.

Move the point at , so the solid line has a slope of .

- What are the coordinates of your point?
- How did you determine where to place your point?
- What is the equation of the line in slope-intercept form?

Move the point at to . Now move the other point so that you have the line .

- What is the slope of the line?
- What are the coordinates of your point?
- Did your method of placing the point change? Explain why or why not.

## Problem 3 – Slope-Intercept Equation

Use the graph at the right to answer the following questions. The points and are on the line.

- What is the slope of the line?
- What is the y-intercept of the line?
- What is the equation of the line?

## Problem 4 – Assessing Understanding

- What kind of line has a slope equal to ?
- What is the slope and intercept of ?
- Name the slope and intercept:
- Name the slope:
- Name the slope:
- True or False: is the intercept of .
- True or False: is the intercept of .
- True or False: is an intercept since .

## Extensions

1. Draw a line on the graph at the right with intercept and any positive slope. Write its equation.

2. Draw a line on this worksheet that goes through and has slope . Write its equation.

3. Draw a horizontal line that goes through . Write its equation.