Question

Which statements are true about the linear inequality y > Three-fourthsx – 2? Select three options.

Answer 1

Answer:

The correct answer choices are B, D, and E.

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Answer 2

Answer:

The graph of y > Three-fourthsx – 2 is a dashed line

One solution to the inequality is (0, 0)

The graph intercepts the y-axis at (0, –2)

Step-by-step explanation:

we have

$y>\frac{3}{4}x-2$

The solution of the inequality is the dashed line above the solid line $y=\frac{3}{4}x-2$

The slope of the dashed line is positive and is equal to $m=\frac{3}{4}$

The y-intercept of the dashed line is (0,-2)

Verify each statement

Option 1) The slope of the line is –2

The statement is false

Because

The slope is equal to $m=\frac{3}{4}$

Option 2) The graph of y > Three-fourthsx – 2 is a dashed line

The statement is true (see the explanation)

Option 3) The area below the line is shaded

The statement is false

Because

The area above the line is shaded

Option 4) One solution to the inequality is (0, 0)

The statement is true

Because

If a ordered pair is a solution of the inequality, then the ordered pair must satisfy the inequality

Substitute the value of x and the value of y of the ordered pair in the inequality

For x=0, y=0

$0>\frac{3}{4}(0)-2$

$0>-2$ ---> is true

so

The ordered pair is a solution of the inequality

Option 5) The graph intercepts the y-axis at (0, –2)

The statement is true (see the explanation)