How do you graph #3x+12y4# on the coordinate plane?

Question

How do you graph #3x+12y>4# on the coordinate plane?

Julia Adams · Accepted Answer

graph{3x + 12y > 4 [-93.7, 93.8, -46.84, 46.94]}
The graph above is the one you wish for.

In this, you want every combination to make a number under four. Let's simplify it a little, first. #x + 4y > 1# For this, you should start with a table. Take -1 for an example. If x is -1, what can y be to be above 1? If we consider that a quarter of the x value makes the y value, the line should be at #x + 4y = -1# and should fill in everything else above, as that fills the specification. Technically, it should NOT include zero but you can claim that it goes one atom above zero. In a real environment. However, try to make it 0.1 over the answer just to make sure you get it right.

Savannah Anderson · Answer

undefined To graph the inequality $3x + 12y > 4$ on the coordinate plane, follow these steps:

1. Begin by graphing the boundary line $3x + 12y = 4$. First, rewrite the equation in slope-intercept form: $y = -\frac{1}{4}x + \frac{1}{3}$.
2. Plot the y-intercept at $(0, \frac{1}{3})$.
3. Find another point on the line by moving along the x-axis and y-axis. For example, when $x = 4$, $y = -\frac{1}{4}(4) + \frac{1}{3} = -1$. So, plot the point $(4, -1)$.
4. Draw a dashed line through these two points to represent the boundary line.

Next, determine which side of the boundary line to shade:
5. Choose a point not on the boundary line. The origin (0,0) is a convenient choice.
6. Substitute the coordinates of the chosen point into the original inequality $3x + 12y > 4$. If the inequality is true, shade the region containing the chosen point. If false, shade the opposite region.
   - For the point (0,0): $3(0) + 12(0) > 4$. This simplifies to $0 > 4$, which is false.
   - Since (0,0) is not in the shaded region, shade the opposite region.

The shaded region represents the solution set of the inequality $3x + 12y > 4$ on the coordinate plane.

How do you graph #3x+12y&gt;4# on the coordinate plane?

How do you graph #3x+12y>4# on the coordinate plane?