Math Problem Statement

What is the slope of the line in this graph?

Solution

To determine the slope of the line in the graph, we can follow these steps:

  1. Identify two points on the line:

    • From the graph, we can choose two clear points where the line crosses grid intersections.
    • One point is (1,2)(1, 2) and another point is (7,6)(7, 6).
  2. Use the slope formula: The formula for the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substituting the points (1,2)(1, 2) and (7,6)(7, 6): m=6271=46=23m = \frac{6 - 2}{7 - 1} = \frac{4}{6} = \frac{2}{3}

Thus, the slope of the line is 23\frac{2}{3}.

However, none of the given answer choices directly match this value. This suggests a possible error in the answer options provided.

Would you like further clarification or more details on this? Here are 5 related questions to consider:

  1. How do you interpret slope in real-world applications?
  2. Can the slope formula be applied to non-linear relationships?
  3. How would the graph change if the slope were negative?
  4. What does a slope of zero signify about the line on a graph?
  5. How do you find the equation of a line if you're given its slope and a point?

Tip: When reading a graph, ensure the selected points are precisely on the grid to avoid errors in calculating slope!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope Calculation

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9