Step 1) Identity two points on the boundary line.
Two such points are (0,7) and (1,5)
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Step 2) Find the slope of the line through those two points
m = (y2-y1)/(x2-x1)
m = (5-7)/(1-0)
m = -2/1
m = -2
The slope is -2
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Step 3) Use the point slope form to get the y = mx+b form
y - y1 = m(x - x1) ..... point slope form
y - 7 = -2(x - 0)
y - 7 = -2x
y = -2x+7
A quicker way is to just note that 7 is the y intercept as visually shown, so b = 7. Which allows us to go from y = mx+b to y = -2x+7
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Step 4) The boundary line is y = -2x+7. This is a dashed line so we will use either a less than sign, or a greater than sign. There will be no "or equal to" as part of the inequality sign.
The shaded region is below the dashed boundary line, so we use a less than sign.
Change y = -2x+7 into y < -2x+7
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Step 5) Change into standard form (optional)
y < -2x+7
2x+y < 7 ... add 2x to both sides
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Final Answer:
y < -2x+7
or
2x+y < 7
The answer will depend on if you want slope intercept form or standard form.
