Math Problem Statement

Find the slope of the line passing through the points (-2, -4) and (2, 2).

Solution

To find the slope of the line, we use the slope formula:

slope=y2y1x2x1\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

From the image, we can see that two points on the line are:

  • (2,4)(-2, -4)
  • (2,2)(2, 2)

Now, apply these values to the slope formula:

slope=2(4)2(2)=2+42+2=64=32\text{slope} = \frac{{2 - (-4)}}{{2 - (-2)}} = \frac{{2 + 4}}{{2 + 2}} = \frac{6}{4} = \frac{3}{2}

Thus, the slope of the line is:

32\frac{3}{2}

Would you like further details or clarification?

Related Questions:

  1. What does the slope represent in real-life scenarios?
  2. How would you find the equation of this line using the slope?
  3. How does the slope affect the steepness of a line?
  4. Can the slope of a vertical line be defined?
  5. What happens to the slope if the line becomes horizontal?

Tip:

The slope of a line is positive if it rises from left to right, and negative if it falls from left to right.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9