# 5.2: Math Man on the Slopes

**At Grade**Created by: CK-12

*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:

\begin{align*}\left \{-0.1, -0.2, -0.4, -9.5, -1.4, 2.7 \right \}\end{align*}

- 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 \begin{align*}y = mx + b\end{align*} and what each letter means. True False

## Problem 2 – Exploring precise slope

Open the file **SLOPE**.

Move the point at \begin{align*}(-2, 4)\end{align*}, so the solid line has a slope of \begin{align*}\frac{2}{3}\end{align*}.

- 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 \begin{align*}(0, 3)\end{align*} to \begin{align*}(1, 0)\end{align*}. Now move the other point so that you have the line \begin{align*}y = x - 1\end{align*}.

- 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 \begin{align*}(0, 1)\end{align*} and \begin{align*}(1, 3)\end{align*} 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 \begin{align*}y-\end{align*}intercept of \begin{align*}y = -3x + 1\end{align*}?
- Name the slope and \begin{align*}y-\end{align*}intercept: \begin{align*}y = \frac{2}{5} x-8\end{align*}
- Name the slope: \begin{align*}y + x = 9\end{align*}
- Name the slope: \begin{align*}y = -4\end{align*}
- True or False: \begin{align*}(0, 6)\end{align*} is the \begin{align*}y-\end{align*}intercept of \begin{align*}y = 2x - 6\end{align*}.
- True or False: \begin{align*}(0, 0)\end{align*} is the \begin{align*}y-\end{align*}intercept of \begin{align*}y = -3x\end{align*}.
- True or False: \begin{align*}(0, 4)\end{align*} is an \begin{align*}x-\end{align*}intercept since \begin{align*}x = 0\end{align*}.

## Extensions

1. Draw a line on the graph at the right with \begin{align*}y-\end{align*}intercept \begin{align*}(0, 4)\end{align*} and any positive slope. Write its equation.

2. Draw a line on this worksheet that goes through \begin{align*}(8,3)\end{align*} and has slope \begin{align*}m = 1\end{align*}. Write its equation.

3. Draw a horizontal line that goes through \begin{align*}(4,-1)\end{align*}. Write its equation.

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