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

The line in the graph starts at the point (9,0)(9, 0) and ends at approximately (9,8)(-9, 8).

Step 1: Calculate the rise (vertical change)

The rise is the difference in the yy-coordinates: Rise=80=8\text{Rise} = 8 - 0 = 8

Step 2: Calculate the run (horizontal change)

The run is the difference in the xx-coordinates: Run=99=18\text{Run} = -9 - 9 = -18

Step 3: Determine the slope

The slope of a line is calculated as: slope=riserun=818=49=49\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{8}{-18} = \frac{4}{-9} = -\frac{4}{9}

Thus, the slope of the line is 49-\frac{4}{9}.

Let me know if you need more details or if you have any questions!


Here are 5 related questions you might consider:

  1. How would the slope change if the line was steeper?
  2. What does a positive slope represent compared to a negative slope?
  3. How can you determine the equation of the line from the graph?
  4. What is the y-intercept of the line in this case?
  5. How would you find the slope if the points were not given but you had the equation of the line?

Tip: When calculating slope, always remember that a negative slope means the line is slanting downwards from left to right!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slope
Linear Equations

Formulas

Slope formula: (rise/run) = (change in y / change in x)

Theorems

Slope of a line theorem

Suitable Grade Level

Grades 8-10