graph the following system of inequalities on the accompanying set of axes and label the solution S.
y>x-4
i got this one.
but how would you graph
y+x> or = to 2.
How do you find the slope and y intercept?
Change it to read (subtract x from both sides
y>-x +0
slope...minus one, intercept zero.
To graph the inequality y + x ≥ 2, you can follow these steps:
1. Begin by graphing the equation y + x = 2 as a solid line. Start by finding the x-intercept and y-intercept of the line.
To find the x-intercept:
Set y to zero and solve for x:
0 + x = 2
x = 2
The x-intercept is (2, 0).
To find the y-intercept:
Set x to zero and solve for y:
y + 0 = 2
y = 2
The y-intercept is (0, 2).
Plot these two points on your graph.
2. Determine which side of the line to shade to represent y + x ≥ 2. To do this, you can choose a test point not on the line and substitute its coordinates for x and y in the inequality.
Let's use the point (0, 0) as a test point.
Substitute its coordinates into the inequality:
0 + 0 ≥ 2
0 ≥ 2
Since the inequality is not true when substituting (0, 0), shade the side of the line that does not include the origin.
3. Finally, label the shaded region as the solution set S.
Regarding the slope and y-intercept:
To find the slope and y-intercept of the line y + x = 2, you can rewrite it in slope-intercept form (y = mx + b) by solving for y.
y + x = 2
y = -x + 2
The slope of the line is -1, and the y-intercept is 2.