Math Problem Statement

Using the linear function graph below, identify the slope (fraction form).

Solution

To find the slope of the line in the graph, we can use the formula for the slope mm between two points on the line:

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

From the graph:

  1. Point 1: The line passes through (-9, -9).
  2. Point 2: The line also passes through (-6, -6).

Calculate the slope:

m=6(9)6(9)=33=1m = \frac{-6 - (-9)}{-6 - (-9)} = \frac{3}{3} = 1

Thus, the slope of the line is m=1m = 1.

Let me know if you'd like any more details or have questions!

Related questions:

  1. What is the equation of the line in slope-intercept form y=mx+by = mx + b?
  2. How do you determine the y-intercept from the graph?
  3. Can the slope be interpreted differently in real-world situations?
  4. What does a slope of 0 indicate about a line?
  5. How do negative slopes affect the direction of a line?

Tip: When finding the slope from a graph, always double-check the coordinates by choosing distinct points where the line crosses grid intersections.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope of a Line

Formulas

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

Theorems

Slope-Intercept Form Theorem

Suitable Grade Level

Grades 8-10