Slope From A Graph | PDF - Free Printable

This is a worksheet from Kuta Software titled "Finding Slope From a Graph." The task is to find the slope of each of the eight lines shown on the coordinate grids.

The slope of a line is calculated using the formula:
Slope (m) = (change in y) / (change in x) = (y₂ - y₁) / (x₂ - x₁)

I will analyze each graph one by one to determine its slope. I will start with problem 1.

Problem 1

- First, look closely: The line passes through several points on the grid. I can pick two clear points to calculate the slope. For example, it passes through (-4, -2) and (4, 2). From left to right, for every 2 units the line goes up, it goes 2 units to the right.
- Next, find information: I don't need an external tool for this; I can calculate it directly from the grid.
- Then, review the findings: The rise (change in y) is 2 and the run (change in x) is 2. So, the slope is 2/2 = 1.

Problem 2

- First, look closely: This line is decreasing. It passes through points like (-4, 4) and (4, -4). For every 2 units it goes down, it goes 2 units to the right.
- Next, find information: Calculating the slope: rise is -2, run is 2. Slope = -2/2 = -1.
- Then, review the findings: The slope is -1.

Problem 3

- First, look closely: The line passes through (-6, -4) and (0, -2). From left to right, it rises 2 units for every 6 units it runs to the right.
- Next, find information: Rise = 2, Run = 6. Slope = 2/6 = 1/3.
- Then, review the findings: The slope is 1/3.

Problem 4

- First, look closely: The line passes through (-4, 5) and (4, -3). It falls 8 units while running 8 units to the right.
- Next, find information: Rise = -8, Run = 8. Slope = -8/8 = -1.
- Then, review the findings: The slope is -1.

Problem 5

- First, look closely: This is a horizontal line. All points have the same y-value (y=0). There is no vertical change.
- Next, find information: Rise = 0, Run = any number. Slope = 0 / run = 0.
- Then, review the findings: The slope is 0.

Problem 6

- First, look closely: This is a vertical line. All points have the same x-value (x=-2). There is no horizontal change.
- Next, find information: Rise = any number, Run = 0. Slope = rise / 0, which is undefined.
- Then, review the findings: The slope is undefined.

Problem 7

- First, look closely: The line passes through (-4, 4) and (0, -2). It falls 6 units while running 4 units to the right.
- Next, find information: Rise = -6, Run = 4. Slope = -6/4 = -3/2.
- Then, review the findings: The slope is -3/2.

Problem 8

- First, look closely: This is another vertical line at x=0 (the y-axis).
- Next, find information: As with problem 6, the run is 0, so the slope is undefined.
- Then, review the findings: The slope is undefined.

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Final Answer

Here are the slopes for each line on the worksheet:

1. Slope = 1
2. Slope = -1
3. Slope = 1/3
4. Slope = -1
5. Slope = 0
6. Slope = Undefined
7. Slope = -3/2
8. Slope = Undefined

The solution involves identifying two points on each line and applying the slope formula `m = (y₂ - y₁) / (x₂ - x₁)`. A horizontal line has a slope of 0, and a vertical line has an undefined slope.