Math Problem Statement

Estimate the slope of the line from its graph.

Solution

To estimate the slope of the line from the graph:

  1. Choose two clear points on the line. From the image:

    • The first point appears to be (0,6)(0, 6) where the line crosses the y-axis.
    • The second point appears to be (6,0)(6, 0) where the line crosses the x-axis.
  2. Use the slope formula: slope=y2y1x2x1\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} Substituting the points (0,6)(0, 6) and (6,0)(6, 0): slope=0660=66=1\text{slope} = \frac{{0 - 6}}{{6 - 0}} = \frac{{-6}}{{6}} = -1

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

Would you like more details or have further questions?

Here are some related questions for practice:

  1. What does the negative slope indicate about the direction of the line?
  2. How would the slope change if the line were steeper?
  3. How do you determine the slope when the line is horizontal?
  4. How does the slope relate to the equation of the line in slope-intercept form?
  5. Can the slope be zero, and if so, what does that mean for the line?

Tip: Remember, the slope is a measure of the steepness of a line. A negative slope indicates the line is decreasing as you move from left to right.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

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

Theorems

Slope of a line theorem

Suitable Grade Level

Grades 7-9