Math Problem Statement

What is the slope of the line passing through the points (-6, -6) and (6, 2)?

Solution

The image shows a graph with a line passing through two points, (6,6)(-6, -6) and (6,2)(6, 2), and the question appears to be asking for the slope of this line.

To find the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), we use the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

For the points given:

  • (x1,y1)=(6,6)(x_1, y_1) = (-6, -6)
  • (x2,y2)=(6,2)(x_2, y_2) = (6, 2)

Substituting these values into the formula: m=2(6)6(6)=2+66+6=812=23m = \frac{2 - (-6)}{6 - (-6)} = \frac{2 + 6}{6 + 6} = \frac{8}{12} = \frac{2}{3}

Therefore, the slope of the line is: 23\boxed{\frac{2}{3}}

Let me know if you'd like more details or have any questions!

Here are some related questions to consider:

  1. How do we interpret the slope of 23\frac{2}{3} in terms of rise over run?
  2. What would be the slope if the line passed through points (6,2)(6, 2) and (6,2)(-6, -2)?
  3. How would the graph look if the slope was 23-\frac{2}{3} instead of 23\frac{2}{3}?
  4. How does changing one of the points affect the slope calculation?
  5. How can you use the slope to find the equation of the line passing through these two points?

Tip: Remember that the slope formula y2y1x2x1\frac{y_2 - y_1}{x_2 - x_1} only works when the two points have different xx-coordinates, otherwise the line is vertical and the slope is undefined.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope
Coordinate Geometry

Formulas

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

Theorems

Slope of a line theorem

Suitable Grade Level

Grades 7-9