Math Problem Statement

What is the slope of the line passing through the points (-1, -2) and (1, 4) on the graph?

Solution

To find the slope of the line on this graph, we can use the slope formula:

slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, we have two points:

  • Point 1: (1,2)(-1, -2)
  • Point 2: (1,4)(1, 4)

Now, applying the formula:

slope=4(2)1(1)=4+21+1=62=3\text{slope} = \frac{4 - (-2)}{1 - (-1)} = \frac{4 + 2}{1 + 1} = \frac{6}{2} = 3

So, the slope of the line is 3.

Would you like further details or explanations?

Here are some related questions you might find useful:

  1. How do you find the slope of a horizontal or vertical line?
  2. What happens if two points are on the same x-coordinate (vertical line)?
  3. How does slope relate to the steepness of a line?
  4. Can slope be a negative value? What does that mean?
  5. What is the difference between slope and y-intercept?

Tip: When calculating the slope between two points, always be careful with signs when subtracting values, especially if they are negative.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Basic concepts of slopes of lines in coordinate geometry

Suitable Grade Level

Grades 7-9