How do you graph #2x+3y4# on the coordinate plane?

Question

How do you graph #2x+3y>4# on the coordinate plane?

Nathan Axel · Accepted Answer

Read explanation below

Move the #2x# to the other side to get #3y> -2x+4#. Then divide by 3 to get #y> -2/3x+4/3#. From here, graph the line #y=-2/3x+4/3#. Then shade in the area which satisfies the inequality (called a half-plane because its area is half of the area of the entire plane). Also, make the line a dotted line to show that it is not included.

Eva Abramson · Answer

undefined To graph the inequality $2x + 3y > 4$ on the coordinate plane, follow these steps:

1. Begin by graphing the boundary line $2x + 3y = 4$. To do this, rewrite the equation in slope-intercept form ($y = mx + b$) by solving for $y$:
$$3y = -2x + 4$$
$$y = -\frac{2}{3}x + \frac{4}{3}$$

2. Plot the boundary line by identifying the y-intercept $(0, \frac{4}{3})$ and using the slope $-\frac{2}{3}$ to find a second point. For example, if you move 3 units to the right from the y-intercept, you move 2 units down. So, another point is $(3, \frac{4}{3} - 2) = (3, -\frac{2}{3})$.

3. Draw a dashed line through these two points to represent the boundary line $2x + 3y = 4$. Since the inequality is strict ($>$), we use a dashed line to indicate that points on the line are not included in the solution set.

4. Determine which side of the line to shade. You can do this by choosing a test point not on the line. A common choice is the origin $(0,0)$. Substitute the coordinates of the test point into the original inequality:
$$2(0) + 3(0) > 4$$
$$0 > 4$$

5. Since $0 > 4$ is false, the origin is not in the solution set. Therefore, shade the side of the line that does not include the origin.

6. Finally, label the shaded region to indicate that it represents the solution set for the inequality $2x + 3y > 4$.

How do you graph #2x+3y&gt;4# on the coordinate plane?

How do you graph #2x+3y>4# on the coordinate plane?