Math Problem Statement

Find the slope of the line from the table below with the points (-3, 5), (-2, 2), (-1, -1), (0, -4), (1, -7).

Solution

To find the slope of the line from the table, we can use the slope formula:

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

We can select any two points from the table. For instance, let's choose the points (3,5)(-3, 5) and (2,2)(-2, 2).

Substitute the coordinates into the formula:

m=252(3)=32+3=31=3m = \frac{{2 - 5}}{{-2 - (-3)}} = \frac{{-3}}{{-2 + 3}} = \frac{{-3}}{{1}} = -3

So, the slope m=3m = -3.

Would you like further details or have any questions? Here are five related questions you might explore:

  1. What does a negative slope represent about the line's direction?
  2. How would you find the slope if given two points not from a table?
  3. Can you explain how the slope would change if the points were reversed?
  4. How does the slope affect the steepness of a line?
  5. What is the relationship between the slope and the linear equation y=mx+by = mx + b?

Tip: When finding the slope, any two distinct points on the line will give you the same result.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope of a Line

Formulas

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

Theorems

Linear equation and slope

Suitable Grade Level

Grade 8