Math Problem Statement

A linear relationship is given in the table.

x y 6 −2 2 2 0 4 −2 6

What is the slope of the relationship? −2 −1 1 2

Solution

To find the slope of a linear relationship, we use the formula for slope, which is:

slope=ΔyΔx=y2y1x2x1\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

You can choose any two points from the table to calculate the slope. Let's use the points (6, -2) and (2, 2).

slope=2(2)26=2+226=44=1\text{slope} = \frac{2 - (-2)}{2 - 6} = \frac{2 + 2}{2 - 6} = \frac{4}{-4} = -1

So, the slope of the relationship is -1.

Would you like further details or an explanation on another concept?

Related questions:

  1. How do you calculate the slope of a line if given the equation?
  2. What does a slope of -1 represent in a real-world scenario?
  3. How can you confirm if the relationship is linear using a graph?
  4. What is the y-intercept of the line passing through these points?
  5. How would you write the equation of this line using slope-intercept form?

Tip: The slope indicates the rate of change between x and y. A negative slope means y decreases as x increases.

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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