Math Problem Statement

What is the slope of the line passing through the points (-4, -4) and (4, 2)?

Solution

To calculate the slope of the line, we use the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, the points provided are (4,4)(-4, -4) and (4,2)(4, 2).

Substituting these into the formula:

m=2(4)4(4)=2+44+4=68=34m = \frac{2 - (-4)}{4 - (-4)} = \frac{2 + 4}{4 + 4} = \frac{6}{8} = \frac{3}{4}

So, the slope of the line is 34\frac{3}{4}.

Would you like further details or have any additional questions?

Here are five related questions:

  1. What does a positive slope signify about the direction of a line?
  2. How would the slope change if the line were steeper?
  3. What is the slope of a horizontal line, and why?
  4. How would you find the equation of the line given two points and the slope?
  5. What happens to the slope if you switch the two points when calculating it?

Tip: A larger slope (steeper line) means the line rises more quickly as it moves from left to right.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear equations

Formulas

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

Theorems

Slope of a line between two points theorem

Suitable Grade Level

Grades 7-9