Math Problem Statement

Find the slope of the line represented by the points (1, 6), (2, 14), (3, 22), (4, 30), (5, 38). These points are linear.

Solution

To find the slope of the line represented by the points given in the table, we use the formula for the slope mm between any two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2): m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

We can use any two points from the table to calculate this. Let's use the first two points (1,6)(1, 6) and (2,14)(2, 14): m=14621=81=8m = \frac{14 - 6}{2 - 1} = \frac{8}{1} = 8

Thus, the slope of the line is 88.

Would you like any further details on this calculation, or do you have any other questions?

Here are some related questions you might consider:

  1. How would the slope change if new points were added?
  2. What does the slope tell us about the nature of the graph?
  3. Can you find the equation of the line using these points?
  4. How do you determine if a point not in the table lies on this line?
  5. What would be the y-intercept of this line based on the table provided?

Tip: Remember, consistency in the results when using multiple pairs of points to calculate slope is a good check that the points indeed lie on a straight line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Linear equation theorem

Suitable Grade Level

Grades 6-8