Math Problem Statement

Find the slope, if it is defined, of the line. If the slope is undefined, state this. The graph of the line is shown in the image.

Solution

The image shows a graph and a prompt asking to find the slope of the given line or state if the slope is undefined.

To calculate the slope of the line (denoted as mm), we use the slope formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are two points on the line.

From the graph, we can identify two clear points:

  • Point 1: (10,10)(-10, -10)
  • Point 2: (10,10)(10, 10)

Now, applying the slope formula: m=10(10)10(10)=10+1010+10=2020=1m = \frac{10 - (-10)}{10 - (-10)} = \frac{10 + 10}{10 + 10} = \frac{20}{20} = 1

Thus, the slope of the line is 11. The correct answer is option A: The slope is 11.

Would you like further details on how to interpret slope or graph lines? Here are some related questions to expand understanding:

  1. What does the slope of a line represent in real-world terms?
  2. How do you determine if a line has an undefined slope?
  3. What is the significance of a slope being positive, negative, zero, or undefined?
  4. Can two lines with the same slope be parallel?
  5. How do you find the equation of a line given its slope and one point?

Tip: The steeper the line, the larger the absolute value of the slope. If a line is horizontal, the slope is zero, and if it is vertical, the slope is undefined.

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Math Problem Analysis

Mathematical Concepts

Slope
Coordinate Geometry

Formulas

m = (y2 - y1) / (x2 - x1)

Theorems

Slope of a Line Theorem

Suitable Grade Level

Grades 7-9