Which of the following inequalities matches the graph? (see attached photo)
A -6x + y < 3
B 6x + y < 3
C 6x - y < -3
D The correct inequality is not listed.
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Looking at the graph, it looks like the y-intercept is (0, 3)
The points (0, 3) and (1, 9) are on the line.
Since we have two points we can calculate the slope: (9 - 3) / (1 - 0) = 6 = m
From (0, 3), we have the y-intercept, b = 3
So the equation of the line is
y = mx + b
y = 6x + 3
Now look at point (0, 0)
Assume inequality is y < 6x + 3
Test (0, 0): Is 0 < 6(0) + 3? 0 < 3 is true, so (0, 0) should be in shaded area. Since it's not, assumption is incorrect and correct inequality is y > 6x + 3
Now see if any of the choices is the same as y > 6x + 3
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6x + y < 3
y < -6x + 3
We have y > 6x + 3, so that's not it.
Let's put our inequality in standard form:
y > 6x + 3
-6x + y > 3
Multiply both sides by -1
Remember the inequality sign changes direction when you multiply or divide both signs by a negative number.
6x - y < -3
That looks like C