Math Problem Statement

Determine the slope of the line below.

Solution

To determine the slope of the line from the graph, we need to find two points that the line passes through. From the graph:

  1. The line passes through the point (0,0)(0, 0) (the origin).
  2. The line also passes through the point (1,1)(1, 1).

The slope mm of a line is calculated using the 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 distinct points on the line. Using the points (0,0)(0, 0) and (1,1)(1, 1):

m=1010=11=1m = \frac{1 - 0}{1 - 0} = \frac{1}{1} = 1

Thus, the slope of the line is 1.

Would you like further details or have any questions?

Related questions:

  1. How do you calculate the slope if the points are not clearly visible?
  2. What is the significance of a slope of 1 in real-life scenarios?
  3. How do negative slopes differ from positive slopes in terms of line direction?
  4. How would you find the slope of a vertical or horizontal line?
  5. Can slope be used to determine if two lines are parallel?

Tip: The slope of a line tells you how steep the line is. A slope of 1 means the line rises 1 unit for every 1 unit it runs horizontally.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear Algebra
Graph Interpretation

Formulas

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

Theorems

Concept of Slope

Suitable Grade Level

Grades 7-9