Math Problem Statement

Find the slope

Find the slope of the line on the graph.

Solution

To find the slope of the line in the graph, we can use the formula:

slope(m)=change in ychange in x=y2y1x2x1\text{slope} (m) = \frac{{\text{change in } y}}{{\text{change in } x}} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

From the image, we can observe two points on the line:

  • The first point is at (2,2)(-2, -2)
  • The second point is at (2,2)(2, 2)

Now, applying the formula:

m=2(2)2(2)=2+22+2=44=1m = \frac{{2 - (-2)}}{{2 - (-2)}} = \frac{2 + 2}{2 + 2} = \frac{4}{4} = 1

Thus, the slope of the line is 1.

Would you like more details on how to calculate the slope, or do you have any further questions?

Here are some related questions for further exploration:

  1. How do you find the slope when given a line in equation form?
  2. What does the slope of a line represent in real-world contexts?
  3. How can you calculate the slope if the line is vertical or horizontal?
  4. What is the significance of positive vs. negative slopes?
  5. How does the slope relate to parallel and perpendicular lines?

Tip: When reading a graph to determine slope, always check for two clearly defined points to make your calculation easier.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9