Math Problem Statement

The table of values shows a linear relationship between x and y. What is the slope of the line represented by the table of values? The options are: A) -8/5, B) -5/8, C) 8/5, D) 5/8.

Solution

To find the slope of the line represented by the table of values, we can use the formula for the slope between two points:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Let's calculate the slope using two points from the table. We will use (7,9)(-7, 9) and (2,1)(-2, 1).

m=192(7)=85m = \frac{1 - 9}{-2 - (-7)} = \frac{-8}{5}

Thus, the slope of the line is:

m=85m = -\frac{8}{5}

The correct answer is A: 85-\frac{8}{5}.


Would you like more details or have additional questions?

Here are 5 related questions for practice:

  1. How would you calculate the slope if given different points from the table?
  2. Can you derive the equation of the line using this slope?
  3. What is the yy-intercept of the line represented by the table?
  4. If the slope were positive, what would that tell you about the line's direction?
  5. How can you verify that all points in the table follow the same linear relationship?

Tip: The slope of a line indicates the rate of change of yy with respect to xx; a negative slope means the line is decreasing!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Rate of Change

Formulas

m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 8-10