Examples with solutions for Graphical Representation: Identifying and reading the graph of a linear function

Exercise #1

Which statement is true according to the graph below?

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Video Solution

Step-by-Step Solution

If we plot all the points, we'll notice that point (3,5) (3,5) is the correct one, because:

x=3,y=5 x=3,y=5

And they intersect exactly on the line where the graph passes.

Answer

The graph passes through (3,5) (3,5) .

Exercise #2

Which statement best describes the graph below?

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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.

Answer

The graph represents an ascending function.

Exercise #3

Choose the correct answer

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Step-by-Step Solution

The blue line is a straight line, therefore it remains constant.

Let's note that the red line is rising because it starts in the negative part (negative values) and rises to the positive part (positive values).

Therefore, the correct answer is D.

Answer

Answers B and C are correct