How am I supposed to graph the linear inequality systems of y => -3x + 1 and y <= -3x - 1?
draw the graphs for the lines as if they were equations.
Now, once you have the line where y equals -3x+1, shade everything above the line, where y is greater than or equal to -3x+1.
It's really quite simple, eh?
Now do the other line and shade above it.
shade below the 2nd line, since y is less
To graph the linear inequality system y >= -3x + 1 and y <= -3x - 1, we can follow these steps:
Step 1: Graph the first equation, y = -3x + 1.
- To do this, we can start by finding two points on the line.
- Choose any x-values (let's say x = 0 and x = 2) and substitute them into the equation to find the corresponding y-values.
- For x = 0: y = -3(0) + 1 = 1, so one point is (0, 1).
- For x = 2: y = -3(2) + 1 = -5, so another point is (2, -5).
- Plot these two points on a coordinate plane and draw a straight line passing through them to represent the equation y = -3x + 1.
Step 2: Graph the second equation, y = -3x - 1.
- Following the same process as in Step 1, find two points on this line.
- For x = 0: y = -3(0) - 1 = -1, so one point is (0, -1).
- For x = 2: y = -3(2) - 1 = -7, so another point is (2, -7).
- Plot these two points on the same coordinate plane and draw a straight line passing through them to represent the equation y = -3x - 1.
Step 3: Identify the shaded regions for the inequalities.
- For the inequality y >= -3x + 1, the shaded region will be above or on the line y = -3x + 1.
- For the inequality y <= -3x - 1, the shaded region will be below or on the line y = -3x - 1.
Step 4: Determine the solution region.
- Find the intersection of the shaded regions from Step 3.
- The overlapping shaded region represents the solution to the linear inequality system.
Note: The solution region might include a portion of or the entire line y = -3x + 1 and y = -3x - 1, depending on the inequality signs (>= and <=).
Now you have successfully graphed the linear inequality system y >= -3x + 1 and y <= -3x - 1.