Math Problem Statement

Find the slope of the line graphed below.

Solution

The task in the image is to find the slope of the graphed line.

Steps to Determine the Slope:

  1. Identify two points on the line: From the graph, we can see two points the line passes through, for example:

    • Point 1: (-3, -5)
    • Point 2: (1, 3)
  2. Use the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substituting the coordinates: m=3(5)1(3)=3+51+3=84=2m = \frac{3 - (-5)}{1 - (-3)} = \frac{3 + 5}{1 + 3} = \frac{8}{4} = 2

Final Answer:

The slope of the line is 2.

If you need more clarification or further steps, feel free to ask!

Here are five follow-up questions:

  1. What does the slope of a line represent in real-world terms?
  2. How do you determine if a slope is positive or negative by looking at a graph?
  3. Can the slope formula be applied to vertical or horizontal lines? Why or why not?
  4. How do changes in the slope affect the steepness of the line?
  5. What is the significance of identifying the slope in a linear equation?

Tip: Always double-check the coordinates you choose when calculating the slope; small errors in signs can lead to incorrect results.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope
Linear Equations

Formulas

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

Theorems

Definition of slope
Properties of linear functions

Suitable Grade Level

Grades 7-9