Math Problem Statement

What is the slope of the line shown in the graph?

Solution

To calculate the slope of the line in the graph, we'll need to use the formula for the slope between two points on a line:

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

From the graph, let's identify two clear points on the line. The line passes through the following points:

  • Point 1: (1,6)(1, -6)
  • Point 2: (6,4)(6, 4)

Now, let's calculate the slope using these points.

slope=4(6)61=4+65=105=2\text{slope} = \frac{4 - (-6)}{6 - 1} = \frac{4 + 6}{5} = \frac{10}{5} = 2

The slope of the line is 22.

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

  1. How do you determine the slope of a vertical line?
  2. What is the equation of a line with a slope of 2 and a y-intercept of -3?
  3. How does the slope relate to the angle of the line?
  4. What does it mean for two lines to have the same slope?
  5. How can you find the slope if only given a graph without points marked?

Tip: Always make sure the points you pick for calculating the slope are accurately placed on the grid intersections for precision.

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Math Problem Analysis

Mathematical Concepts

Algebra
Analytic Geometry
Linear Equations

Formulas

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

Theorems

Slope of a line in Cartesian coordinates

Suitable Grade Level

Grades 8-10