Math Problem Statement

The points in the table lie on a line. Find the slope of the line. The points are (1, 2), (3, 10), (5, 18), and (7, 26).

Solution

To find the slope of the line given by the points in the table, we can use the slope formula:

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

Let's take two points from the table. For simplicity, we can use the first two points:

  • Point 1: (1,2)(1, 2)
  • Point 2: (3,10)(3, 10)

Substitute the coordinates into the slope formula:

slope=10231=82=4\text{slope} = \frac{10 - 2}{3 - 1} = \frac{8}{2} = 4

Therefore, the slope of the line is 4.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

  1. What is the slope if you use points (5,18)(5, 18) and (7,26)(7, 26)?
  2. How do you interpret the slope in a real-world context?
  3. Can the slope ever be negative? Under what conditions?
  4. How would the slope change if the points represented a vertical line?
  5. What is the y-intercept of the line based on the points given?

Tip: When finding the slope, make sure to choose any two distinct points on the line; the slope will always be the same regardless of which pair you pick.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Slope of a Line

Formulas

Slope Formula: (y2 - y1) / (x2 - x1)

Theorems

Slope Theorem

Suitable Grade Level

Grades 7-9