Math Problem Statement

Enter the slope of the line as a reduced fraction. If the slope is undefined, write undefined.

Solution

To find the slope of the line shown in the image, we will use the slope formula:

slope (m)=ΔyΔx=change in ychange in x\text{slope (m)} = \frac{\Delta y}{\Delta x} = \frac{\text{change in } y}{\text{change in } x}

Let's identify two points on the line:

  1. Point 1: (10,5)(-10, 5)
  2. Point 2: (0,5)(0, -5)

Now, calculate the change in yy and xx:

Δy=55=10\Delta y = -5 - 5 = -10 Δx=0(10)=10\Delta x = 0 - (-10) = 10

So the slope is:

m=1010=1m = \frac{-10}{10} = -1

The slope of the line is 1-1.

Would you like further clarification or details?

Here are 5 questions that might help deepen your understanding:

  1. How do you determine the points on a line from a graph?
  2. Can the slope of a vertical line be calculated in the same way?
  3. How would you interpret the slope in real-world contexts?
  4. What happens if the slope is positive instead of negative?
  5. How can you verify the slope using different points on the same line?

Tip: Always check for correct points on the graph by looking where the line crosses grid intersections for accuracy.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope of a Line

Formulas

Slope formula: m = (change in y) / (change in x)

Theorems

Slope formula theorem

Suitable Grade Level

Grades 7-9