Answer:
6 > 2x + y
To find the slope and y-intercept for this linear inequality, we need to write it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the given inequality, we get:
y > -2x + 6
Comparing this with y = mx + b, we can see that the slope is -2 and the y-intercept is 6.
So, the slope is m = -2 and the y-intercept is b = 6.
To graph this linear inequality, we can draw the line y = -2x + 6 (which has a slope of -2 and y-intercept of 6) as a dashed line (since y > -2x + 6, not y = -2x + 6). Then we shade the region above the line, since all the points in that region satisfy the inequality y > -2x + 6.
x < 3y - 6
Again, we need to write this inequality in slope-intercept form to find the slope and y-intercept. Rearranging, we get:
3y > x + 6
Dividing both sides by 3, we get:
y > (1/3)x + 2
So, the slope is m = 1/3 and the y-intercept is b = 2.
To graph this linear inequality, we draw the line y = (1/3)x + 2 (which has a slope of 1/3 and y-intercept of 2) as a dashed line (since x < 3y - 6, not x = 3y - 6). Then we shade the region below the line, since all the points in that region satisfy the inequality x < 3y - 6.