Analyzing the Graph: Discover the Slope and Intercept of a Linear Line

Linear Functions with Slope Direction

Which statement best describes the graph below?

xy

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Step-by-step written solution

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1

Understand the problem

Which statement best describes the graph below?

xy

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Step-by-step solution

To solve this problem, let's analyze the given graph:

  • The graph shows a straight line plotted on a coordinate grid.
  • The line is drawn from the lower-left corner to the upper-right corner. This indicates that for increasing values of x x , the corresponding y y values also increase.

According to the properties of linear graphs:

  • A line with a positive slope rises from left to right, which indicates an ascending function.
  • A line with a negative slope falls from left to right, which indicates a descending function.
  • A line with a zero slope is horizontal, indicating a constant function.

Given that the line in the graph rises as x x increases, it has a positive slope. Therefore, it represents an ascending function.

Thus, the correct statement about the graph is: The graph represents an ascending function.

3

Final Answer

The graph represents an ascending function.

Key Points to Remember

Essential concepts to master this topic
  • Slope Rule: Positive slope means line rises from left to right
  • Visual Check: Follow the line: lower-left to upper-right = ascending function
  • Verification: As x x increases, y y values also increase āœ“

Common Mistakes

Avoid these frequent errors
  • Confusing slope direction with steepness
    Don't focus only on how steep the line looks = missing the direction! A steep line going down still has negative slope. Always trace the line from left to right to determine if it's ascending or descending.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

xy

FAQ

Everything you need to know about this question

How can I tell if a line is ascending just by looking at it?

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Use the left-to-right rule! Start at the left side of the graph and follow the line to the right. If the line goes upward, it's ascending (positive slope). If it goes downward, it's descending (negative slope).

What's the difference between ascending and increasing functions?

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They mean the same thing! An ascending function is also called an increasing function. Both terms describe when y y values get larger as x x values increase.

Can a line be both ascending and descending?

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No, a straight line has constant slope throughout. It's either ascending (positive slope), descending (negative slope), or constant (zero slope). Only curved functions can change from ascending to descending.

What if the line is perfectly horizontal?

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A horizontal line represents a constant function. The y y value stays the same no matter what x x is. This has zero slope - it's neither ascending nor descending.

Does a steeper line mean it's more ascending?

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Steepness affects the rate of increase, but not whether it's ascending. A gentle upward slope and a steep upward slope are both ascending functions - one just increases faster than the other.

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