SOLUTION: Hello, I need help with the following problem: Find a linear inequality with the following solution set. Each grid line represents one unit. The link to the solution set imag

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Question 1044368: Hello,
I need help with the following problem:
Find a linear inequality with the following solution set. Each grid line represents one unit. The link to the solution set image is: http://latex.artofproblemsolving.com/6/4/d/64d8e4d2124c96770af292773d0a587a247b8718.png. (Give your answer in "standard form" +ax%2Bby%2Bc%3E0+ or +ax%2Bby%2Bc%3E=0+ where +a+, +b+, and +c+ are integers with no common factor other than +1+.)
Thanks,
Nicole

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

first find equation of a red line using points (0,1) and (1,1)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (0,1) and (1,0)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (0,1) and (x%5B2%5D,y%5B2%5D) is the second point (1,0))


m=%280-1%29%2F%281-0%29 Plug in y%5B2%5D=0,y%5B1%5D=1,x%5B2%5D=1,x%5B1%5D=0 (these are the coordinates of given points)


m=+-1%2F1 Subtract the terms in the numerator 0-1 to get -1. Subtract the terms in the denominator 1-0 to get 1



So the slope is

m=-1





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-1=%28-1%29%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=1 (these values are given)



y-1=-x%2B%28-1%29%280%29 Distribute -1


y-1=-x%2B0 Multiply -1 and 0 to get 0%2F1. Now reduce 0%2F1 to get 0

y=-x%2B0%2B1 Add 1 to both sides to isolate y


y=-x%2B1 Combine like terms 0 and 1 to get 1

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Answer:



So the equation of the line which goes through the points (0,1) and (1,0) is:y=-x%2B1


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=1


Notice if we graph the equation y=-x%2B1 and plot the points (0,1) and (1,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-x%2B1 through the points (0,1) and (1,0)


Notice how the two points lie on the line. This graphically verifies our answer.




so, your equation in standard form is x%2By-1=0
since you need a linear inequality with the following solution set, it will be x%2By-1%3E0 where a=1, b=1, and c=-1