Math Problem Statement

What is the slope of the graph below?

Solution

To find the slope of the graph, we can use the formula for slope:

slope=ΔyΔx=riserun\text{slope} = \frac{\Delta y}{\Delta x} = \frac{\text{rise}}{\text{run}}

Looking at the graph, the line passes through the points (4,2)(-4, -2) and (4,2)(4, 2). Using these points:

slope=2(2)4(4)=2+24+4=48=12\text{slope} = \frac{2 - (-2)}{4 - (-4)} = \frac{2 + 2}{4 + 4} = \frac{4}{8} = \frac{1}{2}

Thus, the slope is 12\frac{1}{2}. The correct answer is d) 1/2.

Would you like further details, or do you have any other questions?

Here are 5 related questions to practice with:

  1. How do you determine the slope if the graph is horizontal?
  2. What is the slope of a vertical line?
  3. How would the slope change if the line were decreasing?
  4. Can two different lines have the same slope? Why?
  5. How do you find the slope between two points without using a graph?

Tip: Always identify two clear points on the line to calculate the slope accurately.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Slope of a Line
Coordinate Geometry

Formulas

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

Theorems

Slope between two points

Suitable Grade Level

Grades 6-8