The graph below represents which system of inequalities? graph of two infinite lines that intersect at a point. One line is solid and goes through the points 0, 2, negative 2, 0 and is shaded in below the line. The other line is dashed, and goes through the points 0, 6, 3, 0 and is shaded in below the line. y < −2x + 6 y ≤ x + 2 y ≤ −2x + 6 y < x + 2 y < 2 over 3x − 2 y ≥ 2x + 2 None of the above

(0,2)(-2,0)
slope = (0 - 2) / -2 - 0) = -2/-2 = 1
(0,2)...x = 0 and y = 2
sub and find b, the y int
2 = 1(0) + b
2 = b
equation is : y = x + 2......solid line, means there is an equal sign....shaded below the line means less then....
ur inequality for this line is : y < = x + 2

(0,6)(3,0)
slope = (0 - 6) / (3 - 0) = -6/3 = -2

y = mx + b
slope(m) = -2
(0,6)...x = 0 and y = 6
sub and find b, the y int
6 = -2(0) + b
6 = b

ur equation is : y = -2x + 6....dashed line means there is no equal sign...and shading below the line means less then...
so ur inequality of this line is : y < -2x + 6

In summary, ur 2 inequalities are : y < = x + 2 and y < -2x + 6

ap8997154 ap8997154 · Answer 2 · 2022-01-27T12:48:20+01:00

To solve the problem we should know about the Equation of a line and slope of a line.

The equations are (y≤ x+2) and (y< -2x+6).

Given to us

One line is solid and goes through the points (0, 2), and (-2, 0) and is shaded below the line.
The other line is dashed, goes through the points (0, 6) and (3, 0), and is shaded below the line.

For the first line,

Given the points (0, 2), and (-2, 0), therefore,

[tex]x_2=0\\y_2=2\\x_1=-2\\y_2=0[/tex]

Substituting the values in the formula of the slope,

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

[tex]m=\dfrac{2-0}{0-(-2)} = \dfrac{2}{2} = 1[/tex]

Substitute the value of slope and a point in the formula of line,

[tex]y = mx+c\\y_2 = mx_2+c\\2 = (1)0 +c\\c = 2[/tex]

Thus, the equation of the line is y=x+2, but as given the line is solid and is shaded below the line. therefore,

y≤ x+2

For the Second line,

Given the points (0, 6) and (3, 0), therefore,

[tex]x_2=0\\y_2=6\\x_1=3\\y_2=0[/tex]

Substituting the values in the formula of the slope,

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

[tex]m=\dfrac{6-0}{0-3} = \dfrac{6}{-3} = -2[/tex]

Substitute the value of slope and a point in the formula of line,

[tex]y = mx+c\\y_2 = mx_2+c\\6 = (-2)0 +c\\c = 6[/tex]

Thus, the equation of the line is y=-2x+6, but as given the line is shaded below the line. therefore,

y< -2x+6

Hence, the equations are (y≤ x+2) and (y< -2x+6).

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