Math Problem Statement

The points in the table lie on a line. Find the slope of the line. | x | 1 | 3 | 5 | 7 | | y | -7 | -2 | 3 | 8 |

Solution

To find the slope of a line, you can use any two points from the given table and apply the slope formula:

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

Let's use the points (1,7)(1, -7) and (3,2)(3, -2) from the table. Applying the formula:

m=2(7)31=2+72=52m = \frac{-2 - (-7)}{3 - 1} = \frac{-2 + 7}{2} = \frac{5}{2}

Thus, the slope of the line is 52\frac{5}{2}.

Do you have any questions or want further details?


Here are 5 related questions:

  1. What is the slope-intercept form of the equation of this line?
  2. Can we use any two points to find the slope of a line?
  3. How do we interpret the slope in practical terms?
  4. How would the slope change if one point is incorrect?
  5. How do we find the equation of a line if we know the slope and a point?

Tip: When choosing points to find the slope, make sure the points are distinct and correctly substituted into the formula.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Slope of a line

Suitable Grade Level

Grades 8-10