How do you graph #y>2x-3#?

Answer 1
You would first graph the line #y=2x-3#, which you can see below:

graph{y=2x-3 [-10, 10, -5, 5]}

Since you have the "greater than" (or#>#) symbol, however, you would have to test an (#x,y#) coordinate value using the equation #y>2x-3#: this is because either the side of the plane "to the left" or "to the right" of this line will consist of the values "greater than".

Note: you should not test coordinate point that is on the line, since the two sides will equal and this will not tell you which side is the right one.

If I test (#0,0#) (usually the easiest point to use), I will get #0 > -3#, which is true. Therefore, the side of the plane with (#0,0#) will be correct.
Additionally, please note that if the equation has a #># or #<# symbol, the line will be dashed (does not include the values on the line). If the equation has a #≥# or #≤#, this will be a solid line as the values on the line are included.

The answer will then look like this: (shaded portion is the "greater than"side of the plane)

graph{y>2x-3 [-10, 10, -5, 5]}

Hope this helps!

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Answer 2

To graph the inequality y > 2x - 3, follow these steps:

  1. Begin by graphing the line y = 2x - 3 as if it were an equation. This line has a slope of 2 and a y-intercept of -3.

  2. Since the inequality is y > 2x - 3, the graph represents all the points where y is greater than 2x - 3.

  3. To determine which side of the line to shade, choose a test point not on the line. The origin (0,0) is a convenient test point.

  4. Substitute the coordinates of the test point into the original inequality. For the point (0,0), the inequality becomes 0 > 2(0) - 3.

  5. Simplify the inequality to see if it's true or false. In this case, 0 > -3 is true.

  6. Since the test point is true for the inequality, shade the side of the line that contains the test point (in this case, above the line).

  7. Draw the shading as a dashed line since the inequality does not include the boundary line (y = 2x - 3) itself.

Your graph should show a dashed line for y = 2x - 3 and shading above that line to represent the region where y is greater than 2x - 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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