Math Problem Statement

What is the slope of the line given by the table?

Solution

To find the slope of the line represented by the table, we need to calculate the slope mm between any two points using the formula for slope:

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

Let’s choose two points from the table. For simplicity, let’s pick the first two points:

  • (x1,y1)=(0,58)(x_1, y_1) = (0, 58)
  • (x2,y2)=(2,54)(x_2, y_2) = (2, 54)

Now, apply the slope formula:

m=545820=42=2m = \frac{54 - 58}{2 - 0} = \frac{-4}{2} = -2

Thus, the slope of the line is 2-2.

The correct answer is: 2-2.

Would you like more details or have any further questions?

Here are five related questions:

  1. What does the slope represent in this context?
  2. Can the slope change if we pick different points from the table?
  3. How do you interpret a negative slope in a linear equation?
  4. What would the equation of the line be, given this slope and a point?
  5. How do we use slope to determine whether a line is increasing or decreasing?

Tip: The slope tells you how much yy changes for every one-unit increase in xx. A negative slope indicates a downward trend.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Slope of a line between two points

Suitable Grade Level

Grades 7-9