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5.2: Math Man on the Slopes

Difficulty Level: 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:

{0.1,0.2,0.4,9.5,1.4,2.7}\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 y=mx+b\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 (2,4)\begin{align*}(-2, 4)\end{align*}, so the solid line has a slope of 23\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 (0,3)\begin{align*}(0, 3)\end{align*} to (1,0)\begin{align*}(1, 0)\end{align*}. Now move the other point so that you have the line y=x1\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 (0,1)\begin{align*}(0, 1)\end{align*} and (1,3)\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 0\begin{align*}0\end{align*}?
• What is the slope and y\begin{align*}y-\end{align*}intercept of y=3x+1\begin{align*}y = -3x + 1\end{align*}?
• Name the slope and y\begin{align*}y-\end{align*}intercept: y=25x8\begin{align*}y = \frac{2}{5} x-8\end{align*}
• Name the slope: y+x=9\begin{align*}y + x = 9\end{align*}
• Name the slope: y=4\begin{align*}y = -4\end{align*}
• True or False: (0,6)\begin{align*}(0, 6)\end{align*} is the y\begin{align*}y-\end{align*}intercept of y=2x6\begin{align*}y = 2x - 6\end{align*}.
• True or False: (0,0)\begin{align*}(0, 0)\end{align*} is the y\begin{align*}y-\end{align*}intercept of y=3x\begin{align*}y = -3x\end{align*}.
• True or False: (0,4)\begin{align*}(0, 4)\end{align*} is an x\begin{align*}x-\end{align*}intercept since x=0\begin{align*}x = 0\end{align*}.

Extensions

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

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

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

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