Math Problem Statement

Which describes the slope of the given line?

Solution

The line in the image slopes downward as it moves from left to right. This indicates that the slope of the line is negative.

The slope mm of a line is calculated as the ratio of the change in the vertical direction (change in yy) to the change in the horizontal direction (change in xx):

m=ΔyΔxm = \frac{\Delta y}{\Delta x}

In this case, the line moves downward (decrease in yy) as xx increases, which confirms the slope is negative.

Would you like more details on how to calculate the exact slope from the graph, or do you have any other questions?

Here are five related questions to deepen your understanding:

  1. How do you find the slope of a line from two given points?
  2. What is the equation of a line in slope-intercept form?
  3. How does the steepness of a line relate to the magnitude of the slope?
  4. Can a vertical line have a slope, and if so, what is it?
  5. How would the graph look if the slope was positive instead of negative?

Tip: The steeper the line, the larger the absolute value of the slope!

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Functions
Slope

Formulas

Slope formula: m = (Δy / Δx)

Theorems

The Slope-Intercept Form

Suitable Grade Level

Grades 7-9