Math Problem Statement

Find the slope of the line.

Solution

To find the slope of the line, we need two points that lie on the line. From the graph, we can clearly identify the following points:

  • Point 1: (5,5)(-5, 5)
  • Point 2: (0,0)(0, 0)

The formula for the slope mm between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is:

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

Substituting the coordinates of the two points:

m=050(5)=55=1m = \frac{0 - 5}{0 - (-5)} = \frac{-5}{5} = -1

So, the slope of the line is 1-1.

Would you like further details or have any questions?

Here are five related questions to expand on this:

  1. How would you find the slope if the line were horizontal or vertical?
  2. What does the negative slope indicate about the direction of the line?
  3. Can the slope of a line be a fraction? What does that represent graphically?
  4. How does the slope relate to the equation of a line in slope-intercept form y=mx+by = mx + b?
  5. How can you determine the slope if the graph was less clear, without exact points?

Tip: A negative slope always means the line decreases as you move from left to right.

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Math Problem Analysis

Mathematical Concepts

Slope
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope theorem

Suitable Grade Level

Grades 8-10