The graph of 2x + 3y > -3 is a dashed line that intersects the axes at points (-³/₂, 0) and (0, -1). The origin (0, 0) is included in the shaded area.
Further explanation
In this problem, we will make the graph of 2x + 3y > -3.
Let us first arrange the equation of the line followed by making a graph of a linear inequality.
Step-1: the x-intercept and the y-intercept
2x + 3y = -3
- For y = 0, we get the x-intercept.
2x + 3(0) = -3
2x = -3, and then divide by two on both sides.
Hence, the x-intercept is [tex]\boxed{x = -\frac{3}{2}} \rightarrow \boxed{ \ (-\frac{3}{2}, 0) \ }[/tex]
- For x = 0, we get the y-intercept.
2(0) + 3y = -3
3y = -3, and then divide by 3 on both sides.
Hence, the y-intercept is [tex]\boxed{y = -1} \rightarrow \boxed{ \ (0, -1) \ }[/tex]
Step-2: graph the inequality
- 2x + 3y = -3 is the boundary line and we draw the line dashed since the equality symbol is " > ".
- Test the point (0, 0), as origin, in 2x + 3y > -3, i.e., [tex]\boxed{2(0) + 3(0) > -3} \rightarrow \boxed{ \ 0 > -3 \ }[/tex] which is true.
- Since the test point results are true, we shade the region which contains the test point.
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Notes:
To graph a linear equality in two variables, follow the steps.
- Draw the boundary line using a dashed line if the inequality symbol is " < or > ", or a solid line if the inequality symbol is " ≤ or ≥ ".
- Choose a test point which is not on the boundary line and substitute it into the equality.
- Shade the region which includes the test point if the resulting inequality is true, and shades the region which does not contain the test point if the resulting inequality is false.
Learn more
- Which is the graph of 2x – 4y > 6? https://brainly.com/question/4408289
- Finding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992
- Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38? https://brainly.com/question/1626676
