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Which of the following statements describe the graph of the solution set for the inequality y = 4x - 3? Select all that apply.

A) The graph line is solid.
B) The graph line is dotted.
C) The graph line passes through the origin.
D) The ordered pair (2,5) is part of the solution set.
E) The shaded region of the graph representing the solution set is to the right of the graph line.

1 Answer

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Final answer:

The graph of the linear equation y = 4x - 3 is a solid line which does not pass through the origin, includes the point (2,5), and has a positive slope. It is not dotted, and there is no shaded region since this is not an inequality.

Step-by-step explanation:

The given inequality is y = 4x - 3. When graphing a linear equation such as this, where y is equal to an expression in x, the graph of the solution set is a single line. Here are some details about the graph:

  • The graph line is solid because the equation uses an equals sign, indicating that all points on the line are part of the solution set.
  • The graph line is not dotted; dotted lines are used for inequalities that do not include the boundary line itself, which is not the case here.
  • The graph line does not pass through the origin. The y-intercept is -3, which can be seen from the equation 4x - 3 where y is 0 when x is 0, resulting in the y-intercept (0, -3).
  • The ordered pair (2,5) is part of the solution set. This can be verified by substituting x with 2 in the equation to get y = 4(2) - 3 which equals 5.
  • The shaded region of the graph representing the solution set would not be to the right or left of the graph line because this is not an inequality but a linear equation. Therefore, there is no shading involved in this graph.

The straight line has a positive slope indicated by the positive coefficient of x, which is 4.

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