Math Problem Statement

What is the slope of this line?

Solution

To find the slope of the line shown in the graph:

Steps to Determine the Slope

  1. Slope formula:
    slope=riserun\text{slope} = \frac{\text{rise}}{\text{run}} Here, "rise" is the vertical change, and "run" is the horizontal change.

  2. Identify two clear points on the graph:

    • The line passes through (8,8)(-8, -8) and (8,4)(8, 4).
  3. Calculate the rise and run:

    • Rise (change in yy): 4(8)=4+8=124 - (-8) = 4 + 8 = 12
    • Run (change in xx): 8(8)=8+8=168 - (-8) = 8 + 8 = 16.
  4. Divide the rise by the run:
    slope=1216=34.\text{slope} = \frac{12}{16} = \frac{3}{4}.

Final Answer:

The slope of the line is 34\frac{3}{4}.


Would you like a further explanation of the slope calculation process or a review of different forms of linear equations? Here are some related questions you might consider:

  1. How do you calculate the slope when given two points?
  2. What does a positive or negative slope tell us about a line?
  3. How can you determine if two lines are parallel or perpendicular?
  4. How do you write the equation of a line using the slope and one point?
  5. What is the difference between a proper fraction and an improper fraction?

Tip: Always check for clear points where the line crosses grid intersections to simplify slope calculations!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line

Formulas

Slope formula: m = (change in y) / (change in x)

Theorems

Definition of slope between two points on a line

Suitable Grade Level

Grade 7-9