Math Problem Statement

What is the slope of the line on the graph?

What is the slope of the line on the graph?

Solution

To find the slope of the line shown in the graph, we can use the slope formula:

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

We need to pick two clear points on the line to apply this formula. From the graph, the two points that appear to be on the line are:

  • Point 1: (8,6)(-8, 6)
  • Point 2: (4,2)(4, 2)

Using these points in the formula:

slope=264(8)=44+8=412=13\text{slope} = \frac{2 - 6}{4 - (-8)} = \frac{-4}{4 + 8} = \frac{-4}{12} = -\frac{1}{3}

Thus, the slope of the line is 13-\frac{1}{3}.

Would you like further details or have any questions?

Here are some related questions you might find useful:

  1. What is the equation of the line in slope-intercept form?
  2. How can you determine the y-intercept from this graph?
  3. What does a negative slope indicate about the direction of the line?
  4. Can you explain the significance of the slope in real-world contexts?
  5. How would the graph change if the slope were positive?

Tip: A negative slope means that as xx increases, yy decreases, and vice versa.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope of a Line

Formulas

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

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 6-9