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5.2: Math Man on the Slopes

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:

$\left \{-0.1, -0.2, -0.4, -9.5, -1.4, 2.7 \right \}$

• 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 $y = mx + b$ and what each letter means. True False

Problem 2 – Exploring precise slope

Open the file SLOPE.

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

• 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 $(0, 3)$ to $(1, 0)$. Now move the other point so that you have the line $y = x - 1$.

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

Extensions

1. Draw a line on the graph at the right with $y-$intercept $(0, 4)$ and any positive slope. Write its equation.

2. Draw a line on this worksheet that goes through $(8,3)$ and has slope $m = 1$. Write its equation.

3. Draw a horizontal line that goes through $(4,-1)$. Write its equation.

Feb 22, 2012

Oct 31, 2014