Math Problem Statement

Find the slope of the line in the graph shown, which passes through points (-4, -2) and (-2, 4).

Solution

To find the slope of the line in the graph, we can follow these steps:

  1. Identify two points on the line: From the graph, we can see that the line passes through the points (4,2)(-4, -2) and (2,4)(-2, 4).

  2. Use the slope formula: The slope mm of a line is given by the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of two points on the line.

  3. Substitute the points: Using the points (4,2)(-4, -2) and (2,4)(-2, 4): m=4(2)2(4)=4+22+4=62=3m = \frac{4 - (-2)}{-2 - (-4)} = \frac{4 + 2}{-2 + 4} = \frac{6}{2} = 3

So, the slope of the line is 3.

Would you like further details or have any questions about this?

Here are some related questions:

  1. How do you calculate the slope if the points are given in decimal form?
  2. What is the meaning of a positive versus a negative slope?
  3. How can you find the slope of a horizontal or vertical line?
  4. How do you calculate the slope if a line passes through the origin?
  5. What are the different ways to express the equation of a line using the slope?

Tip: The slope of a line is a measure of its steepness. A larger absolute value of the slope means the line is steeper!

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope of a Line
Coordinate Geometry

Formulas

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

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 7-9