Math Problem Statement

What is the slope of the line?

Solution

To calculate the slope of the line, we can use the slope formula:

slope=y2y1x2x1\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

Here, the two points are given as:

  • Point 1: (5,4)(-5, 4)
  • Point 2: (2,1)(2, 1)

Let's substitute the coordinates into the formula:

slope=142(5)=37=37\text{slope} = \frac{{1 - 4}}{{2 - (-5)}} = \frac{{-3}}{{7}} = -\frac{3}{7}

Thus, the slope of the line is 37-\frac{3}{7}, which corresponds to option D.

Would you like any further clarification on this process?

Here are some related questions you can explore:

  1. How do you interpret the slope in the context of a real-life problem?
  2. What happens to the slope if the line is horizontal or vertical?
  3. How do you calculate the slope from a table of values?
  4. Can the slope be positive, negative, or zero? What do these values mean geometrically?
  5. How does the slope relate to the concept of rate of change?

Tip: Always remember that the slope represents the steepness or incline of a line, with the sign indicating whether it rises or falls.

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Math Problem Analysis

Mathematical Concepts

Linear Relationships
Slope of a Line
Coordinate Geometry

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-9