Math Problem Statement

what is the slope of the line

What is the slope of the line?

Solution

To find the slope of the line from the given graph, I'll need to identify two points on the line and then calculate the slope using the formula:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

Let's extract the coordinates of two visible points from the graph:

  • First point: (0,1)(0, -1)
  • Second point: (3,1)(3, 1)

Now, applying the slope formula:

m=1(1)30=23m = \frac{1 - (-1)}{3 - 0} = \frac{2}{3}

Thus, the slope of the line is 23\frac{2}{3}.

Would you like more details or have any questions?

Here are some related questions to expand on this:

  1. How can the slope be interpreted in real-life situations?
  2. What happens to the graph if the slope becomes negative?
  3. How can we graph a line if only the slope and one point are given?
  4. How does changing the slope affect the steepness of the line?
  5. Can we find the equation of this line using its slope and one point?

Tip: When identifying points on a line, always choose those that lie directly on grid intersections for accuracy.

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Slope of a Line

Formulas

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

Theorems

Slope of a line between two points

Suitable Grade Level

Grades 7-9