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

In the provided image, we are asked to draw and interpret the rise and run of the line, and determine the slope of the line in its simplest form. Let's break it down:

  1. Identifying the Points: The line on the graph starts at point (9,4)(-9, -4) and ends at point (1,3)(1, 3).

  2. Finding the Rise (vertical change): The rise is the difference in the y-coordinates of the two points: Rise=y2y1=3(4)=7\text{Rise} = y_2 - y_1 = 3 - (-4) = 7

  3. Finding the Run (horizontal change): The run is the difference in the x-coordinates of the two points: Run=x2x1=1(9)=10\text{Run} = x_2 - x_1 = 1 - (-9) = 10

  4. Calculating the Slope: The slope mm of a line is the ratio of the rise to the run: m=RiseRun=710m = \frac{\text{Rise}}{\text{Run}} = \frac{7}{10}

Thus, the slope of the line is 710\frac{7}{10}.

Would you like any further details or clarification on how we determined the slope?

Here are 5 related questions to explore further:

  1. How do you calculate the slope between two points in general?
  2. What does a positive slope indicate about the direction of a line?
  3. How can you tell if a slope is undefined?
  4. How would the slope change if the line moved downward instead of upward?
  5. Can you find the equation of the line using the slope and one point?

Tip: Always remember that slope is a ratio of vertical change (rise) to horizontal change (run), which helps describe the steepness and direction of a line.

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Math Problem Analysis

Mathematical Concepts

Slope of a Line
Algebra
Linear Equations

Formulas

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

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 7-9