Math Problem Statement

What is the slope of the points on the graph

What is the slope of the points on the graph?

Solution

To determine the slope of the line on the graph, we can use the slope formula:

slope=y2y1x2x1\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}

Here, we need to identify two points on the line. From the image, we can visually estimate two points:

  1. One point appears to be at (4,2)(-4, -2).
  2. Another point seems to be at (2,2)(2, 2).

Now, applying the slope formula:

slope=2(2)2(4)=2+22+4=46=23\text{slope} = \frac{2 - (-2)}{2 - (-4)} = \frac{2 + 2}{2 + 4} = \frac{4}{6} = \frac{2}{3}

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

Would you like a more detailed explanation of how the slope is calculated?

Here are 5 related questions:

  1. How do you find the equation of a line given its slope and a point on it?
  2. What is the difference between positive and negative slope?
  3. How can you determine the slope if the graph is steeper or flatter?
  4. How do parallel and perpendicular slopes relate to each other?
  5. What is the interpretation of slope in real-world problems?

Tip: When identifying points from a graph, always double-check coordinates to ensure accuracy, especially if they lie between grid lines.

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Math Problem Analysis

Mathematical Concepts

Slope of a Line
Coordinate Geometry

Formulas

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

Theorems

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Suitable Grade Level

Grades 7-10