# 5.1: Points & Lines & Slopes

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

*This activity is intended to supplement Algebra I, Chapter 4, Lesson 3.*

## Problem 1 – Coordinates of Points

Open the *CabriJr* app by pressing **APPS**. Open a new file and make sure the axes are displayed. Place a point, \begin{align*}R\end{align*}

1. Explain what is common to all points on the \begin{align*}x-\end{align*}

2. Explain what is common to all points on the \begin{align*}y-\end{align*}

Delete points \begin{align*}R\end{align*}

Complete the sentences by writing *positive* or *negative*.

3. A point is in Quadrant 1 (top right) when its \begin{align*}x-\end{align*}

4. A point is in Quadrant 2 (top left) when its \begin{align*}x-\end{align*}

5. A point is in Quadrant 3 (bottom left) when its \begin{align*}x-\end{align*}

6. A point is in Quadrant 4 (bottom right) when its \begin{align*}x-\end{align*}

Draw two lines through point \begin{align*}P\end{align*}

7. What is this relationship between the coordinates of point \begin{align*}P\end{align*}

## Problem 2 – Lines, Equations, and Slopes

Delete or hide the segments and measurements. Draw a line connecting \begin{align*}P\end{align*}

Look for relationships between the slope and equation as you change the line by grabbing and dragging point \begin{align*}P\end{align*}

8. When dragging the line by point \begin{align*}P\end{align*}

9. When dragging the line itself, what is changing in the equation?

10. Drag point \begin{align*}Q\end{align*}

## Problem 3 – Slopes of Parallel and Perpendicular Lines

Open the Cabri Jr. file **PARALLEL**. Drag the lines by points \begin{align*}P\end{align*}

11. What can you say about the slopes of two parallel lines?

Open the Cabri Jr. file **PERPENDI**. Again drag the lines to investigate the relationship between the slopes.

12. What can you say about the slopes of two perpendicular lines?

Use the **Calculate** tool to see what happens when the slopes of two perpendicular lines are multiplied together. Select one slope measurement, press \begin{align*}\times\end{align*}

Now, change the lines by grabbing and dragging point \begin{align*}P\end{align*}

13. What do you observe about the product of the slopes?