Math Problem Statement

A line passes through the points in this table. x y 12 50 16 36 20 22 24 8 What is the slope of the line?

Solution

To find the slope of a line passing through two points, we use the slope formula:

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

Using the points (12,50)(12, 50) and (16,36)(16, 36) as an example:

m=36501612=144=3.5m = \frac{36 - 50}{16 - 12} = \frac{-14}{4} = -3.5

Thus, the slope of the line is m=3.5m = -3.5.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

  1. How would the equation of the line look in slope-intercept form?
  2. What is the y-intercept of this line?
  3. Can you find the equation of the line using two different points from the table?
  4. How would you graph this line using the slope and y-intercept?
  5. What is the relationship between slope and the steepness of the line?

Tip: When calculating slope, make sure to choose any two points on the line; the slope remains consistent regardless of which points you select.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope of a Line Theorem

Suitable Grade Level

Grades 8-10