Question

Which statements are true about the graph of y < 2/3x + 1?

Check all that apply.
The slope of the line is 1.
The line is solid.
The area below the line is shaded.
A solution to the inequality is (2, 3).
The x-intercept of the boundary line is (, 0).

Answer 1

Answer:

 Option (3) and (5) is correct.

3) The area below the line is shaded.

5) The x-intercept of the boundary line is (-1.5,0)

Step-by-step explanation:

 Given inequality $y<\frac{2}{3}x+1$

We have to check out of given statements which statements are true about the graph of $y<\frac{2}{3}x+1$

We first plot the graph for the given inequality

And we will check all given statement one by one,

1) The slope of the line is 1.

Slope of a line is the derivative of given equation with respect to x,

Thus, slope of  given inequality $y<\frac{2}{3}x+1$ is

$\frac{dy}{dx}=\frac{2}{3}$

Thus, statement is false.

2) The line is solid.

No, as the inequality has only less than sign so it will be a dotted line.

3) The area below the line is shaded.

Yes, it is clear from the graph the area below is shaded.

4) A solution to the inequality is (2, 3)

No, from graph the point (2,3) lies outside the shaded region.

5) The x-intercept of the boundary line is (-1.5,0)

Yes , x - intercept where y = 0

The x-intercept of the boundary line is (-1.5,0)

 

Thus, Option (3) and (5) is correct.

 

Answer 2

The option (3) and (5) are correct and satisfy the given inequality.

Given data:

The equation of graph is, $y<2/3x+1$.

(1)

Slope of a line is the derivative of given equation with respect to x. Then differentiating the equation as,

$\dfrac{dy}{dx}=\dfrac{2}{3}$

Clearly slope of line is 2/3 not 1.  Hence, the statement is false.

(2)

The line is not solid because as the inequality has only less than sign so it will be a dotted line. Hence, the statement is false.

(3)

From the graph attached below, it is clear that the area below the line is shaded. Thus, the statement is true.

(4)

Since, the point (2,3) in the graph attached below will lie outside the shaded portion. Therefore, (2,3) is not the solution and the statement is false.

(5)

The x-intercept of the boundary line is (-1.5,0)  as per the attached graph. Therefore, the statement is true.

Thus, we can conclude that the option (3) and (5) are correct and satisfy the given inequality.

Learn more about the inequality here:

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