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 graph shows a line passing through two points, which will help us calculate the slope by determining the "rise" and "run." The slope mm of a line is calculated as:

m=riserun=y2y1x2x1m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, the line appears to pass through two points, approximately (1,10)(1, -10) and (6,4)(-6, 4).

  1. Calculate the rise: The rise is the difference in the y-coordinates: rise=y2y1=4(10)=4+10=14\text{rise} = y_2 - y_1 = 4 - (-10) = 4 + 10 = 14

  2. Calculate the run: The run is the difference in the x-coordinates: run=x2x1=61=7\text{run} = x_2 - x_1 = -6 - 1 = -7

  3. Calculate the slope: m=147=2m = \frac{14}{-7} = -2

So, the slope of the line is 2-2.

Would you like more details or explanations? Here are 5 related questions:

  1. How is slope related to the steepness of a line?
  2. What does a negative slope indicate about the direction of a line?
  3. How can you find the equation of a line if you know its slope and a point?
  4. What is the difference between positive, negative, zero, and undefined slopes?
  5. How would the slope change if the line were vertical?

Tip: Always remember that the slope represents the change in yy (rise) over the change in xx (run).

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Coordinate Geometry

Formulas

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

Theorems

Slope formula

Suitable Grade Level

Grades 7-10