Math Problem Statement

Find the slope

Find the slope

Solution

To determine the slope of the line from the image, let's analyze the graph:

  1. The slope (mm) is calculated using the formula: m=ΔyΔx=RiseRunm = \frac{\Delta y}{\Delta x} = \frac{\text{Rise}}{\text{Run}}

  2. Based on the image:

    • The line passes through two visible points:
      • The first point: approximately (3,2)(-3, -2)
      • The second point: approximately (1,2)(-1, 2)
  3. Calculate the change in yy (Δy\Delta y) and change in xx (Δx\Delta x): Δy=2(2)=4,Δx=1(3)=2\Delta y = 2 - (-2) = 4, \quad \Delta x = -1 - (-3) = 2

  4. The slope is: m=ΔyΔx=42=2m = \frac{\Delta y}{\Delta x} = \frac{4}{2} = 2

Final Answer:

The slope of the line is 2.

Would you like further details on this?


Expanding your understanding:

  1. What does the slope represent in real-world applications?
  2. How does the slope of a line relate to its steepness?
  3. Can you identify slopes from equations like y=mx+by = mx + b?
  4. How would a negative slope change the direction of the line?
  5. What is the slope of a horizontal or vertical line?

Tip: Always check the units or scaling of the graph to ensure your calculations are accurate.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope
Coordinate Geometry

Formulas

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

Theorems

Concept of Slope in Linear Equations

Suitable Grade Level

Grades 7-9