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Marina86 [1]
3 years ago
13

Which inequality matches the graph?

Mathematics
1 answer:
Papessa [141]3 years ago
8 0

Given:

The dotted boundary line passes through the points (-3,-8), (1,-2) and (9,10).

Above line is shaded.

To find:

The inequality for the given graph.

Solution:

Consider any two points on the line. Let the two points are (1,-2) and (9,10). So, the equation of the line is:

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-(-2)=\dfrac{10-(-2)}{9-1}(x-1)

y+2=\dfrac{10+2}{8}(x-1)

y+2=\dfrac{12}{8}(x-1)

y+2=\dfrac{3}{2}(x-1)

Multiply both sides by 2.

2(y+2)=3(x-1)

2y+4=3x-3

2y-3x=-3-4

-3x+2y=-7

Above line is shaded and the boundary line is a dotted line. So, the sign of inequality must be >.

-3x+2y>-7

This inequality is not in the equations. So, multiply both sides by -1 and change the inequality sign.

(-3x+2y)(-1)

3x-2y

Therefore, the correct option is D.

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