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Graph the equation y = 2x - 5 using an interactive graphing calculator. Which of the following statements are true based on the graph?

A. The line increases from left to right.
B. The line crosses the x-axis at 2.5.
C. The line crosses the y-axis at 5.
D. As the input increases, the output decreases.
E. The line does not enter.

1 Answer

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Final answer:

The graph of y = 2x - 5 shows a line with a positive slope, increasing as it goes from left to right, crossing the x-axis at 2.5 and the y-axis at -5. The line's slope indicates a rise of 2 units in y for every 1-unit increase in x.

Step-by-step explanation:

When we graph the equation y = 2x - 5 using an interactive graphing calculator, we can determine the characteristics of the line represented by the equation.

  • A. The line increases from left to right.
  • B. The line crosses the x-axis at 2.5. This is because when y=0, 0 = 2x - 5, solving for x gives us x = 2.5.
  • C. The line does not cross the y-axis at 5; rather, it crosses at -5 because when x=0, y = 2(0) - 5 = -5.
  • D. As the input (x-value) increases, the output (y-value) increases as well due to the positive slope of the line which is 2.
  • E. The statement about the line not entering is unclear and may be disregarded as a typo or an irrelevant part of the question.

The slope of the line is the ratio of the rise to the run on a graph. A positive slope means that for every increase in the x-value, there is a corresponding increase in the y-value. Thus, with a slope of 2, the line rises 2 units on the y-axis for every 1 unit it moves to the right on the x-axis. The line's y-intercept is -5, which is the point where the line crosses the y-axis. None of the information given indicates a negative slope or that the output decreases as the input increases, nor is there a y-intercept of 50 as suggested by the reference material. The statements made with a y-intercept of 50 do not apply to the equation y = 2x - 5.

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