Math Problem Statement

What is the slope of this line?

Solution

To find the slope of a line, we use the formula for slope:

slope=ΔyΔx=y2y1x2x1\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

From the graph, I can see that the line passes through two clear points:

  1. (8,8)(-8, -8)
  2. (4,4)(4, 4)

Let's calculate the slope using these two points:

slope=4(8)4(8)=4+84+8=1212=1\text{slope} = \frac{4 - (-8)}{4 - (-8)} = \frac{4 + 8}{4 + 8} = \frac{12}{12} = 1

Thus, the slope of the line is 11.

Would you like more details on how the slope was calculated? Here are some related questions:

  1. How is the slope interpreted in real-life situations?
  2. What happens if the line is horizontal or vertical?
  3. Can the slope be negative, and what would that mean?
  4. How do you find the equation of a line given the slope and a point?
  5. What is the relationship between slope and parallel/perpendicular lines?

Tip: Always ensure to pick points that are easy to read from the graph when calculating the slope.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations
Slope

Formulas

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

Theorems

Concept of slope in a linear equation

Suitable Grade Level

Grades 6-8