Graph a linear inequality in two variables

Which graph best describes the solution to this set of inequalities?
x + y ≤ 6
x + 2y ≤ 8

To graph x + y ≤ 6
y ≤ -x + 6   {got in "slope-intercept form"}
Graph the boundary line y = -x + 6
- put a point on 6 on the y-axis {the y-intercept}
- from there, move down 1 and right 1 and put another point down
- draw a solid line through the two points
- shade down on the y-axis because of the ≤ sign

To graph x + 2y ≤ 8
2y ≤ -x + 8   {subtracted x from each side}
y ≤ (-1/2)x + 4   {divided each side by 2}

Graph the boundary line y = (-1/2)x + 4
- put a point on the y-intercept, 4
- from there, move down 1 and right 2 and put another point down
- draw a solid line through the two points
- shade down on the y-axis because of the ≤ sign

The overlap of the two graphs is the
solution set.

Answer is D.)

Ask Algebra House