Math Problem Statement

Describe the slope of the line shown in the graph.

Solution

The graph shows a line passing through two points: one near (4,2)(-4, -2) and another near (2,4)(2, 4).

To describe the slope, we calculate it using the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

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

Using the approximate coordinates (4,2)(-4, -2) and (2,4)(2, 4), we have:

slope=4(2)2(4)=66=1\text{slope} = \frac{4 - (-2)}{2 - (-4)} = \frac{6}{6} = 1

Therefore, the slope of the line is 1, meaning the line rises by 1 unit for every 1 unit it moves horizontally, indicating a positive and linear increase.

Would you like further clarification or more details on the topic? Here are some related questions to explore:

  1. How do you interpret a positive slope in real-life scenarios?
  2. What is the difference between positive, negative, zero, and undefined slopes?
  3. How would the graph change if the slope were greater than 1?
  4. How do we find the slope of a line that is vertical or horizontal?
  5. How does the slope relate to the equation of a line in slope-intercept form?

Tip: When calculating slopes, it's helpful to remember that a positive slope means the line moves upwards as you go from left to right.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

slope = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9