Math Problem Statement

Find the slope of the line graphed below.

Solution

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

m=y2y1x2x1m = \frac{{y_2 - y_1}}{{x_2 - x_1}}

This formula uses two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) on the line. From the graph, we can observe the following two points:

  1. The first point appears to be (1,1)(1, 1).
  2. The second point is around (4,2)(4, -2).

Using these coordinates:

m=2141=33=1m = \frac{{-2 - 1}}{{4 - 1}} = \frac{{-3}}{{3}} = -1

So, the slope of the line is -1.

Would you like further clarification or details? Here are five follow-up questions related to this topic:

  1. How do we interpret a negative slope in terms of the graph's behavior?
  2. What are the steps for finding the slope if the points are not integer values?
  3. What is the meaning of a slope of 0 in a graph?
  4. How can you identify if two lines are parallel just by looking at their slopes?
  5. How does changing the slope affect the steepness of the line?

Tip: The slope of a line tells you how much the line rises or falls for every unit of horizontal movement.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10