Question 152939: Please help me solve and sketch the solution to this inequality on a graph.
y < -1/3x + 2
Thank you for helping me!!!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Consider this, if your equation was:
y = -1/3x + 2
Notice, instead of the < sign, it is replaced by an = sign.
This is simply an equation of a line in the "slope intercept" form:
y = mx + b
where
m is the slope
b is the y-intercept at (0,b)
.
So, for your equation:
y = -1/3x + 2
m (slope) is -1/3 (that is, rise of -1 and run of 3).
b (y-intercept) is at (0,2)
.
To plot the line above on graph paper, you could:
Step 1: plot the y-intercept -- draw a dot at (0,2)
Step 2: using the slope (rise/run) -- starting from the dot above, (since rise is -1) go down one unit, and (since run is 3) go right three units -- place another dot here.
Step 3: connect the two dots and you've just plotting the line.
.
Now, let's talk about that < sign. Let's modify the work done above.
.
Your original equation of:
y < -1/3x + 2
Because the equation above does NOT have an = sign, instead of a SOLID line connecting the two dots -- make it a dotted line instead. AND, finally, because it is a < sign, SHADE the area UNDER this dotted line -- that's it, you're done.
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