Math Problem Statement

Find the slope based on the provided table of x and y values: (x: -2, -1, 0, 1; y: 5, 3, 1, -1).

Solution

To find the slope between two points on a graph, we use the slope formula:

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

Looking at the table, you have the following points:

  • Point 1: (2,5)(-2, 5)
  • Point 2: (1,3)(-1, 3)

Using the slope formula with these points: m=351(2)=21+2=21=2m = \frac{3 - 5}{-1 - (-2)} = \frac{-2}{-1 + 2} = \frac{-2}{1} = -2

Thus, the slope is 2-2.

Would you like further clarification or additional details on how this was calculated?

Here are 5 related questions you could explore:

  1. How would the slope change if we picked two different points from the table?
  2. What does a negative slope tell you about the relationship between xx and yy?
  3. How do you calculate the slope for vertical or horizontal lines?
  4. Can the slope of a line be zero? If so, in what scenario?
  5. What is the significance of the slope in real-world applications like distance-time graphs?

Tip: A steeper negative slope means the line decreases faster as xx increases.

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Math Problem Analysis

Mathematical Concepts

Slope of a Line
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope theorem: The slope of a line measures the rate of change between two points on the line.

Suitable Grade Level

Grades 6-8