Question

Which inequality matches the graph?

X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Dotted line on graph has positive slope and runs through negative 3, negative 8 and 1, negative 2 and 9, 10. Above line is shaded.

−2x + 3y > 7
2x + 3y < 7
−3x + 2y > 7
3x − 2y < 7

Answer 1

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.

$(-3x+2y)(-1)<-7(-1)$

$3x-2y<7$

Therefore, the correct option is D.