Question

Is there a way to remember the steps?
Graph the linear inequality.
y≥3x

Answer 1

Err basically when you graph it should not be a dotted line, but a solid line. Also it is similar to the y=mx+b formula the less than or equal to sign takes the place of the equal sign. so plug in 3x into the formula. You will notice that 3x is the slope of the formula okay? You won't have the + b at the end which is the "Y" intercept where it crosses the y axis. So just put the 3 over 1 to make it into 3/1 which is the rise/run formula. start from zero go up three points and across to the right 1 time. Repeat and then connect the dots with a line and then show me what you get.

Answer 2

this is our inequality that we want to graph :\[y \ge 3x\]
Step 1:
look at the sign and determine whether you will be drawing a broken/dotted line \[(> or <)\] or a solid line \[(\ge or \le)\]
Step 2:
Find your intercepts.
To find your y-intercept, let x = 0.
y = 3x= 3(0) = 0
So this means that when x = 0 , y = 0
Find your x-intercept , let y = 0
3x = 0 , x = 0
So again when y = 0 , x = 0

Step 3:
Pick a random point.
E.g. when x = 1, what will y = ?
y = 3x
y = 3(1) = 3
So we get the point (1, 3)
Now when x = -1, y =?
y = 3(-1) = -3
So we get the point (-1,-3)

Plot the two points on the graph and draw a line:


Now to know which side to shade, pick a random point and check if it satisfies your inequality.
So let's pick (1,2)
So when x = 1 , y = 2. Sub these into your inequality and we get:
\[y \ge 3x \rightarrow 2\ge 3\]
Which is false right? Because 2 does not equal to and is not greater than 3.
Therefore the point (1,2) will NOT be included (therefore the side which includes this point will NOT be shaded)