How do you graph #-y+3x

Question

How do you graph #-y+3x<=6#?

Eli Assouline · Accepted Answer

There are a couple possible approaches. Here's one.

I finding leading negative signs hard to read, so I would begin by rewriting the inequality as: #3x-y <= 6#

Start by graphing the equation: #3x-y = 6#

For this equation, it is straightforward to find the intercepts, so that's now I would graph this one. (If you prefer to put it in slope-intercept form first, do that.)

#(0, -6)# and #(2, 0)# are the intercepts so draw the line through those two points. So you get this:

graph{3x-y = 6 [-10, 10, -5, 5]}

The line #3x-y = 6# cuts the plane into two regions. In one region, the value of #3x-y# is #<6#, in the other it is #>6#. Our job now is to figure out which side is which so we can stay on the "less than 6" side.

I see that the point #(0,0)# (the origin) is not on the graph of the equation, so I'll just check to see if that side is the #<6# or #>6# side. #3(0)-(0)=0-0=0# which is less than #6#. So the region above the line must be the #<6# side of the line.

The inequality we're looking at wants the # <=6# side, so we shade that side. (If you wanted to double check, you could pick a point above the line. Say #(5, 0)# or (10, 0)# and make sure that #3x - y < 6#

Your graph should look like this:

graph{3x-y<=6 [-10, 10, -5, 5]}

Hazel Anglin · Answer

undefined To graph the inequality -y + 3x ≤ 6, follow these steps:

1. Begin by graphing the boundary line y = 3x + 6. To do this, plot the y-intercept at (0, 6) and then use the slope (rise over run) of 3 to find additional points. For example, if you move one unit to the right (run) and three units up (rise), you get the point (1, 9). Connect these points with a solid line because the inequality includes the equal sign (≤).

2. Since the inequality includes ≤, the region below the boundary line is shaded to represent all the points that satisfy the inequality.

3. You can test a point not on the boundary line, such as (0, 0), to determine which side of the line to shade. Substitute the x and y values into the inequality: -0 + 3(0) ≤ 6. This simplifies to 0 ≤ 6, which is true. Since (0, 0) is below the boundary line, shade the region below the line.

4. The shaded region represents the solution to the inequality -y + 3x ≤ 6.

How do you graph #-y+3x&lt;=6#?

How do you graph #-y+3x<=6#?