Math Problem Statement

a line passes through the points (4,-1) and (2,3) what is the slope of the line

Solution

The slope of a line passing through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated using the formula:

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

Substituting the points (4,1)(4, -1) and (2,3)(2, 3) into the formula:

m=3(1)24=3+124=42=2m = \frac{3 - (-1)}{2 - 4} = \frac{3 + 1}{2 - 4} = \frac{4}{-2} = -2

So, the slope of the line is m=2m = -2.

Would you like more details or have any further questions?

Here are 5 related questions to explore this topic:

  1. How do you find the equation of a line given two points?
  2. What is the slope of a vertical line?
  3. What does the slope represent in the context of a graph?
  4. Can the slope of a line be zero? If so, under what conditions?
  5. How do you graph a line if you know the slope and a point?

Tip: The slope tells you how steep a line is and whether it rises or falls as you move from left to right on a graph.

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Math Problem Analysis

Mathematical Concepts

Algebra
Geometry
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

Slope-Intercept Theorem
Linear Equation

Suitable Grade Level

Grades 7-9