Math Problem Statement

Find the slope of the line shown in the graph.

Solution

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

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

From the image, I can see that the line passes through two points:

  • One point appears to be at (2,1)(-2, -1)
  • Another point is at (2,3)(2, 3)

Now, let's calculate the slope using these two points:

m=3(1)2(2)=3+12+2=44=1m = \frac{3 - (-1)}{2 - (-2)} = \frac{3 + 1}{2 + 2} = \frac{4}{4} = 1

So, the slope of the line is 1.

Would you like further details or have any questions?

Here are 5 related questions you might find useful:

  1. What is the significance of the slope in real-world problems?
  2. How do you calculate the slope of a horizontal line?
  3. What happens to the slope if the line is vertical?
  4. Can the slope of a line be negative? If so, in what cases?
  5. How do you find the equation of a line given its slope and one point on the line?

Tip: The slope can help you understand how steep a line is and in which direction it goes (upward or downward).

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Slopes of Lines

Formulas

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

Theorems

Slope formula in Cartesian planes

Suitable Grade Level

Grades 7-10