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

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" or where , , and are integers with no common factor other than .)
Thanks,
Nicole

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

first find equation of a red line using points (,) and (,)

Solved by pluggable solver: Finding the Equation of a Line

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

So the slope is

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

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

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

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

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

so, your equation in standard form is
since you need a linear inequality with the following solution set, it will be where , , and
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