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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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.

Mathematics
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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
@mathstudent55 so it would be B?

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B is 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

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