Math Problem Statement

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

Solution

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

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

Looking at the graph, two points on the line are marked:

  • (2,2)(2, 2)
  • (4,4)(4, 4)

Using these two points:

  • x1=2x_1 = 2, y1=2y_1 = 2
  • x2=4x_2 = 4, y2=4y_2 = 4

Now, applying the values into the slope formula:

m=4242=22=1m = \frac{4 - 2}{4 - 2} = \frac{2}{2} = 1

Thus, the slope of the line is 1.

Would you like more details on how to interpret slope from graphs?

Here are 5 related questions for further exploration:

  1. What does a slope of 1 signify in terms of the relationship between xx and yy?
  2. How would the slope change if the points were different but still on the same line?
  3. What is the slope of a horizontal line?
  4. How do you find the slope when points have negative coordinates?
  5. Can the slope be zero, and what does that indicate?

Tip: A line with a positive slope like this one indicates that as xx increases, yy also increases.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope of a Line

Suitable Grade Level

Grades 7-9