Sol A 6 Finding Slope And Rate Of Change - Fill Online, Printable ... - Free Printable

I'll solve the problems on this worksheet step by step, explaining each solution.

First, let me look at the overall structure of the worksheet to understand what's being asked.

The worksheet has three main sections:
1. Plot points and draw a line through them, then determine if the slope is positive, negative, zero, or undefined.
2. Find the slope of the line that passes through given points.
3. A word problem about finding slope from rise and run.

Let me start with the first section - plotting points and determining slope direction.

For problem 1: Points (1, -4) and (5, -8)
- When we plot these, as x increases from 1 to 5, y decreases from -4 to -8
- This means the line slopes downward from left to right
- Therefore, the slope is negative

For problem 2: Points (-3,0) and (-3,5)
- Both points have the same x-coordinate (-3), different y-coordinates
- This creates a vertical line
- Vertical lines have undefined slope

For problem 3: Points (1,2) and (2,1)
- As x increases from 1 to 2, y decreases from 2 to 1
- The line slopes downward from left to right
- Therefore, the slope is negative

For problem 4: Points (-4,-3) and (6,-3)
- Both points have the same y-coordinate (-3), different x-coordinates
- This creates a horizontal line
- Horizontal lines have zero slope

Now let me move to the second section - finding the actual slope values using the formula:
Slope = (y₂ - y₁) / (x₂ - x₁)

For problem 5: Points (2,4) and (7,9)
- Slope = (9 - 4) / (7 - 2) = 5 / 5 = 1

For problem 6: Points (4,4) and (1,5)
- Slope = (5 - 4) / (1 - 4) = 1 / (-3) = -1/3

For problem 7: Points (-2,0) and (5,8)
- Slope = (8 - 0) / (5 - (-2)) = 8 / 7

For problem 8: Points (3,0) and (0,4)
- Slope = (4 - 0) / (0 - 3) = 4 / (-3) = -4/3

For problem 9: Points (-6,-6) and (-2,-2)
- Slope = (-2 - (-6)) / (-2 - (-6)) = 4 / 4 = 1

For problem 10: Points (-4,6) and (11,-2)
- Slope = (-2 - 6) / (11 - (-4)) = (-8) / 15 = -8/15

Now for the third section - the graphs:

Problem 11: Looking at the graph, it appears to be a line going up from left to right, so positive slope. From the grid, I can see it rises 2 units for every 1 unit it runs, so slope = 2/1 = 2.

Problem 12: This line goes down from left to right, so negative slope. It appears to fall 1 unit for every 2 units it runs, so slope = -1/2.

Problem 13: This is a horizontal line, so slope = 0.

Problem 14: This is a vertical line, so slope is undefined.

Finally, problem 15: A ramp has a rise of 10 feet and a run of 50 feet.
- Slope = rise / run = 10 / 50 = 1/5 = 0.2

All problems are now solved. Let me summarize the answers:

Section 1 (slope direction):
1. Negative
2. Undefined
3. Negative
4. Zero

Section 2 (slope values):
5. 1
6. -1/3
7. 8/7
8. -4/3
9. 1
10. -8/15

Section 3 (graphs):
11. 2
12. -1/2
13. 0
14. Undefined

Problem 15: 1/5 or 0.2