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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

Respuesta :

nobillionaireNobley
Given that the graph runs through (-3, -8) and (1, -2) and (9, 10).

Taking any two points from the graph, we find the equation of the graph as follows:

[tex] \frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1} \\ \\ \frac{y-(-8)}{x-(-3)} = \frac{-2-(-8)}{1-(-3)} \\ \\ = \frac{-2+8}{1+3} = \frac{6}{4} = \frac{3}{2} \\ \\ \frac{y+8}{x+3} = \frac{3}{2} \\ \\ \Rightarrow2(y+8)=3(x+3) \\ \\ \Rightarrow2y+16=3x+9 \\ \\ \Rightarrow3x-2y=7[/tex]

Because, above the line is shaded, therefore, the correct inequality matching the graph is 3x - 2y < 7

The inequality that matches the graph can be evaluated by using equation of line using two points and the inequallity is given by: (3x - 2y < 7).

Given :

  • 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 points: (-3,-8), (1,-2), and (9,10).

The inequality that matches the graph can be evaluated by using equation of line using two points.

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]    ----- (1)

Now, select any two points from (-3,-8), (1,-2), and (9,10) and put the values in equation (1).

[tex]\dfrac{y+8}{x+3}=\dfrac{-2+8}{1+3}[/tex]

[tex]\dfrac{y+8}{x+3}=\dfrac{3}{2}[/tex]

[tex]2(y+8)=3(x+3)[/tex]

[tex]3x - 2y = 7[/tex]

It is also given that the 'above line is shaded' therefore the inequality is given by: (3x - 2y < 7)

For more information, refer the link given below

https://brainly.com/question/11612965

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