Math Problem Statement

Find the slope of the line graphed below.

Solution

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

slope(m)=y2y1x2x1\text{slope} \, (m) = \frac{y_2 - y_1}{x_2 - x_1}

Step 1: Identify two clear points on the line.

From the graph, we can select the following two points where the line intersects grid points:

  • Point 1: (3,3)(-3, 3)
  • Point 2: (3,2)(3, -2)

Step 2: Apply the slope formula.

m=233(3)m = \frac{-2 - 3}{3 - (-3)}

Simplify the numerator and denominator:

m=56m = \frac{-5}{6}

Step 3: Interpret the result.

The slope of the line is:

m=56m = -\frac{5}{6}

This negative slope indicates that the line decreases (falls) as it moves from left to right.


Do you want further explanation, or have any questions about this?

5 Related Questions:

  1. How do you find the slope when given two points?
  2. What does a positive slope versus a negative slope indicate?
  3. How is the slope of a horizontal or vertical line different?
  4. How does the slope relate to the equation of a line?
  5. Can you calculate the slope from a table of points?

Tip: The steeper the slope (in absolute value), the faster the line increases or decreases.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

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

Theorems

-

Suitable Grade Level

Grades 8-10