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# Find a linear inequality with the following solution set. Each grid line represents one unit. [asy] size(200); fill((-1,-5)--(-5,-5)--(-5,5

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Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in "standard form"  or  where   and  are integers with no common factor greater than 1.)

Aug 28, 2019

#1
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The points (3, 1)  and (1, -2)   are on the graph

The slope of the line through these points is given by :   [-2-1] / [ 1 - 3]  = -3/ -2  = 3/2

So.....the equation of this line is

y  = (3/2)(x - 3) + 1           multiply through by 2

2y =  3( x - 3)  + 2

2y = 3x - 9 + 2

-3x + 2y  = - 7             multiply through by -1

3x  - 2y  =  7

Since we have a dotted line than we have that either

3x - 2y  > 7        or         3x - 2y  <  7

Note that (0, 0)  is in the shaded area....this will satisfy   3x - 2y   < 7   Aug 29, 2019
#2
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Can you find the equation of the red line?

It has a slope of 3/2 and a y-intercept of -7/2.

Can you solve from there?

You are very welcome!

:P

Aug 29, 2019