Math Problem Statement

Draw a line representing the 'rise' and a line representing the 'run' of the line. State the slope of the line in simplest form.

Solution

To determine the slope of the line shown in the graph, we need to calculate the "rise" (vertical change) and "run" (horizontal change) between two points on the line.

Step 1: Identify Two Points

Looking at the line, we can identify two points:

  • First Point: (8,10)(-8, 10)
  • Second Point: (8,6)(8, -6)

Step 2: Calculate the Rise and Run

  • Rise (Vertical Change): From 10 to -6, which is 610=16-6 - 10 = -16.
  • Run (Horizontal Change): From -8 to 8, which is 8(8)=168 - (-8) = 16.

Step 3: Calculate the Slope

The slope mm of the line is given by: m=RiseRun=1616=1m = \frac{\text{Rise}}{\text{Run}} = \frac{-16}{16} = -1

Conclusion

The slope of the line in its simplest form is 1\boxed{-1}.


Do you want further details or have any questions?

Here are some related questions you might explore:

  1. How do you find the slope of a line from a graph?
  2. What does a negative slope indicate about the direction of a line?
  3. How can you find the equation of a line using the slope and a point?
  4. How would the slope change if the line was steeper?
  5. What are some real-world applications of understanding slope?

Tip: The slope is a measure of how steep a line is; a negative slope means the line goes down as it moves from left to right!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Basic principles of slope calculation

Suitable Grade Level

Grades 7-9