Given the system of inequalities:

4x – 5y < 1

one-halfy – x < 3

which shows the given inequalities in slope-intercept form?

y < four-fifthsx – one-fifth

y < 2x + 6

y > four-fifthsx – one-fifths

y < 2x + 6

y > negative four-fifthsx + one-fifth

y > 2x + 6

slope intercept form is option 3 -

slope intercept form is option 4 -

Step-by-step explanation:

Given : The system of inequalities and

To find : Which shows the given inequalities in slope-intercept form?

Solution :

The slope intercept form is where m is the slope and b is y-intercept.

First inequality is

Now we take y to one side by subtracting 4x both side,

Divide both side by 5,

Multiply both side by -1,

So, Option 3 is correct.

Second inequality is

Now we take y to one side by adding x both side,

Multiply both side by 2,

So, Option 4 is correct.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

the answer is d

step-by-step explanation: