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Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 ⁢ x + 2 B. y ≥ 2 ⁢ x + 2 C. y < 2 ⁢ x + 2 D.

Respuesta :

Considering the given linear function, the inequality graphed is:

B. [tex]y \geq 2x + 2[/tex].

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:

m = (4 - 2)/(2 - 1) = 2.

Thus the equation of the line is:

y = 2x + 2.

The left-side of the line is the values above the line, hence the inequality is:

B. [tex]y \geq 2x + 2[/tex].

More can be learned about linear functions at https://brainly.com/question/24808124

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