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 problem requires drawing the "rise" and "run" to represent the slope of the line and then stating the slope in its simplest form. Based on the image:

  1. The given line has a negative slope because it decreases from left to right.
  2. To determine the slope:
    • Rise is the change in the vertical direction (up or down).
    • Run is the change in the horizontal direction (left or right).

Steps to Solve:

  1. Pick two points on the line where it crosses grid intersections. For example:
    • The line passes through (-6, 8) and (0, 0).
  2. Calculate the "rise":
    • From (0, 0) to (-6, 8), the vertical change is 80=88 - 0 = 8.
  3. Calculate the "run":
    • The horizontal change is 0(6)=60 - (-6) = 6.
  4. The slope (mm) is: m=riserun=86=43.m = \frac{\text{rise}}{\text{run}} = \frac{-8}{6} = -\frac{4}{3}.

Thus, the slope of the line is 43-\frac{4}{3}.

Would you like further clarification or help plotting the rise and run? Here are some related questions:

  1. How can I simplify fractions in slope calculations?
  2. What does the negative sign in a slope indicate geometrically?
  3. Can we determine slope using any other formula or method?
  4. How would the slope change if the line were rotated?
  5. What are some real-life examples where slope is applied?

Tip: Always double-check grid intersections when selecting points for rise and run calculations to ensure accuracy.

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Math Problem Analysis

Mathematical Concepts

Slope
Coordinate Geometry

Formulas

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

Theorems

Slope of a Line

Suitable Grade Level

Grades 8-10