Math Problem Statement

Find the slope, if it is defined, of the line. If the slope is undefined, state this.

Solution

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

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

From the graph, we can pick two clear points that the line passes through. Let's choose the points (10,8)(-10, -8) and (10,8)(10, 8).

Now, apply the slope formula:

slope=8(8)10(10)=8+810+10=1620=45\text{slope} = \frac{8 - (-8)}{10 - (-10)} = \frac{8 + 8}{10 + 10} = \frac{16}{20} = \frac{4}{5}

Thus, the slope is 45\frac{4}{5}.

So, the correct answer is A. The slope is 45\frac{4}{5}.

Would you like more details or further explanations? Here are five related questions you might find helpful:

  1. How do you determine if a slope is positive or negative?
  2. What is the significance of a slope of zero?
  3. How does an undefined slope differ from a slope of zero?
  4. Can you find the equation of the line using the slope and one point?
  5. How can the slope formula be applied in three-dimensional space?

Tip: When the line moves upward from left to right, the slope is positive, as seen in this example!

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

Theorems

Slope formula

Suitable Grade Level

Grades 7-9