Math Problem Statement

The graph of a function is shown on the coordinate plane. Identify the slope of the function.

Solution

To determine the slope of the function from the graph:

  1. Identify two clear points on the line. From the image, the line passes through:

    • Point 1: (6,6)(-6, -6)
    • Point 2: (6,6)(6, 6)
  2. Use the slope formula: slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} Substituting the coordinates: slope=6(6)6(6)=1212=1\text{slope} = \frac{6 - (-6)}{6 - (-6)} = \frac{12}{12} = 1

The slope of the line is 1.

Do you need more details or have any questions?

Here are 5 related questions to explore further:

  1. How does changing the slope affect the steepness of a line?
  2. What is the slope of a horizontal line?
  3. How would the slope change if one of the points was different?
  4. What is the relationship between slope and rate of change?
  5. How do you calculate the slope for a vertical line?

Tip: The slope represents the rate at which yy changes with respect to xx. For a slope of 1, for every unit increase in xx, yy increases by the same amount.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

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

Theorems

Slope of a line

Suitable Grade Level

Grades 6-8