Math Problem Statement

answer

Find the slope of the line shown in the graph.

Solution

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

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

Looking at the graph, two points on the line are approximately:

  • (7,7)(-7, -7)
  • (7,7)(7, 7)

Using these points in the slope formula:

slope=7(7)7(7)=7+77+7=1414=1\text{slope} = \frac{7 - (-7)}{7 - (-7)} = \frac{7 + 7}{7 + 7} = \frac{14}{14} = 1

So, the slope of the line is 1.

Would you like more details or have any questions? Here are five related questions:

  1. How do you find the slope of a vertical or horizontal line?
  2. What is the significance of a slope of 0?
  3. How does a positive slope compare to a negative slope in terms of direction?
  4. Can the slope formula be used for curved lines?
  5. How does changing the slope affect the steepness of a line?

Tip: When finding the slope from a graph, choose points that are easy to read and far apart to reduce errors in calculation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Slope
Linear Equations

Formulas

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

Theorems

Slope of a straight line theorem

Suitable Grade Level

Grades 6-8