Math Problem Statement

The points in the table lie on a line. Find the slope of the line.

Solution

The table shows four points that lie on a line. To find the slope of the line, we can use the formula for the slope between any two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):

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

Let's pick two points from the table: (3,0)(-3, 0) and (2,2)(2, 2).

Applying the slope formula:

slope=202(3)=25\text{slope} = \frac{2 - 0}{2 - (-3)} = \frac{2}{5}

The slope of the line is 25\frac{2}{5}.

Do you want more details or have any questions?

Here are 5 related questions:

  1. Can you verify the slope by using different pairs of points from the table?
  2. How do we know that the points lie on a straight line?
  3. What does the slope represent in real-world terms?
  4. What would happen to the slope if the line were steeper?
  5. Can the slope of a line ever be negative?

Tip: The slope of a line tells us how much the yy-value changes for a given change in the xx-value.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Slope of a Line

Suitable Grade Level

Grades 7-9