What is 2y + x < 12 as an inequality graphed?

Answer 1

You effectively draw the line 2y + x = 12, but answers that lie on the line are not valid, so for example, y=2, x=8 will give = 12, which is not < 12 so therefore incorrect. Once you have drawn the line 2y + x = 12 (use dotted lines to indicate it is not a solution), then shade in the area below the line, which is the feasible region. Pick a point, e.g. (0,0) and test it in the inequality if you are unsure!

Answer 2

What is 2y + x < 12 as an inequality graphed?
2y < -x +12
y < -x/2 + 6
For the moment, assume y=-x/2 +6. Then,
When x = 0 , y= 6 so plot the point (0,6)
When y = 0, x = 12, so plot the point (12,0)
Now draw a dashed straight line that passes through (0,6) and (12,0) and extend it as far as you wish in both directions

Now shade all the area below the dashed line and this shaded area will contain all the points that satisfy the inequality.

Answer 3

the equation 2y+x=12 represents st. line cuts the x_axis at the point (12,0) and the y_axis at (0,6)
all the points under this line belonges to the solution set of the inequality 2y+x<12

Answer 4

When you change it to slope-intercept form, you get

y<-1/2 x + 6

That is a dashed line with a slope of -1/2 and a y-intercept of (0,6). This graph is true for all points below the line.

Answer 5

Subtract x from both sides:
2y<-x+12

Divide 2 from both sides:
y<-1/2x+6

The graph is telling you that y will be less than 6.

Answer 6

<-------------------O
<--------|-----------|-->
_____0_____6

Hope this works!