Question

Which is the graph of the linear inequality x – 2y > –6?

Answer 1

Answer:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

The first step is writing in the general form of the first order equation

y = f(x) or y > f(x) or y < f(x)

And

f(x) = ax + b

In which a is the slope.

We have that:

x - 2y > -6

-2y > -6 - x

When multiplying by -1, the signal changes, from > to <

2y < x + 6

y < 0.5x + 3

The slope is positive, since 0.5 is positive.

Since it is y lesser than, it is everything below and to the right of f(x) is painted.

The line is dashed because this is just lesser, not lesser or equal.

The correct answer is:

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Answer 2

Answer:

D. On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, 2) and (4, 4). Everything below and to the right of the line is shaded.

Step-by-step explanation:

Given inequality is x-2y > -6

Now assume that x-2y = -6

The above equation is a line which meets the x-axis at (-6,0) and y-axis at (0,3)

We know that the slope of the line joining the points (a , b) and (c , d) is

$m=\frac{d-b}{c-a}$

now the slope the given line is $m=\frac{3-0}{0-(-6)}$ = $\frac{1}{2}$.

The given line has a positive slope.

The given two points in all the options is (-4 , 2) and (4 , 4).

For any point above this line say (0 , 4) does not satisfy the given inequality.

So all the points lied below the given line towards the origin satisfy the given inequality.

Now for deciding wether it is a solid or dashed straight line the following is used,

If the inequality is > or < then it is a dashed line otherwise (in the case of ≤ and  ≥) it is a solid line.

So from all the above we can conclude that the option is

On a coordinate plane , a dashed straight line which has a positive slope and goes through (-4 , 2) and (4 , 4).Everything below and to the right of the line is shaded.