Will you please explain the steps I must take in order to graph these linear inequalities?
Graph each system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
1. y < 2x - 1
y > 2
2. x < 3
y > x -2
3. y => 3x
3x + y => 3
4. 2x - 4y <= 8
y > x -2
in general if you have
y > mx + b, you would shade in the region above the line y = mx + b
y < mx + b , you would shade in the region below the
line y = mx + b
if the inequality contains ≥ or ≤ , the would include the boundary line itself and make it solid
if you have just > or < , use a dotted line to set the boundary.
for y > c, shade in the region above y = c, a horizontal line
for y < c, shade in below
for x > c , shade in the region to the right of the vertical line x = c
for x < c, shade in the region to the left of y = c
so let's do 3. , you do the rest
y ≥ 3x, the line y = 3x would be included.
two points on y = 3x are (0,0) and (3,9)
plot the points and draw a solid line through them
Shade in the region above y = 3x
3x+y ≥ 3
y ≥ -3x + 3
two points on that one are (0,3) and (3,-6)
draw a solid line through those points, and extend the line to suit your graph
Shade in the region above that line as well.
Your solution is the region shaded by both.
Now just pick any point in that common region for your first part answer, then two point anywhere outside the common region to show a non-solution.
Since a point has to satisfy both inequations, it must be in the common region.
A point could satisfy one inequation but not the other, so it would NOT be a solution.
your graph should look like this
http://www.wolframalpha.com/input/?i=plot++y+%3D+3x+%2C+y+%3D+-3x+%2B+3+
with the triangular region at the top shaded in
Sure! To graph linear inequalities, we typically follow these steps:
Step 1: Start by graphing the boundary line for each inequality. Treat the inequality as an equation and graph it as if it were an equal sign.
Step 2: Determine whether the boundary line should be drawn as a solid line or a dashed line. If the symbol in the inequality is "less than" or "greater than," use a dashed line. If the symbol is "less than or equal to" or "greater than or equal to," use a solid line.
Step 3: Select a test point not on the boundary line and substitute its coordinates into the inequality. If the inequality is true for the test point, shade the region containing it. If it is false, shade the region that does not contain the test point.
Step 4: Repeat steps 1-3 for each inequality in the system.
I'll go ahead and explain how to graph each of the given systems of inequalities and provide two ordered pairs that are solutions, as well as two that are not solutions.
1. Graphing the inequalities:
a. y < 2x - 1:
Start by drawing the line y = 2x - 1. Use a dashed line since the inequality is "less than."
b. y > 2:
Draw a horizontal line at y = 2. Use a solid line since the inequality is "greater than."
2. Selecting test points:
Choose two points that are not on the boundary lines. For example, you can use (0, 0) and (1, 3).
3. Determining solutions:
Substitute the coordinates of the test points into the inequalities:
a. (0, 0):
y < 2x - 1 -> 0 < 2(0) - 1 -> 0 < -1 (false)
y > 2 -> 0 > 2 (false)
This point is not a solution to either inequality.
b. (1, 3):
y < 2x - 1 -> 3 < 2(1) - 1 -> 3 < 0 (false)
y > 2 -> 3 > 2 (true)
This point is a solution to the second inequality.
4. Shade the solution region:
Shade the region that satisfies both inequalities. In this case, no region satisfies both inequalities since there is no overlapping shaded area.
Repeat the above steps for the remaining systems of inequalities (2, 3, and 4) to graph them and find the solutions and non-solutions.