Question

putting it all together
answer these open - ended questions on your own or with others to form deeper math connections.
task 2
how do the signs of the rise and run affect the graph of the line?
task 3
how does the steepness of the line change when the rise gets closer to 0? when the run approaches 0?
task 4
what happens when the rise is 0?
task 5
why does a vertical line have an \undefined slope\?

Explanation:

For Task 2: The sign of the rise and run determines the direction of the line. A positive rise and positive run gives an upward - sloping line from left to right, a positive rise and negative run gives a downward - sloping line from left to right, and vice - versa.
For Task 3: When the rise gets closer to 0, the line becomes flatter. When the run approaches 0, the line becomes steeper.
For Task 4: When the rise is 0, the line is horizontal.
For Task 5: The slope is defined as $\frac{rise}{run}$. For a vertical line, the run is 0. Division by 0 is undefined, so the slope of a vertical line is undefined.

Answer:

Task 2: The sign combination determines line direction.
Task 3: Rise close to 0 makes line flatter; run close to 0 makes line steeper.
Task 4: The line is horizontal.
Task 5: Because slope formula has division by 0 (run = 0 for vertical line).