Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?

They are parallel.
They are perpendicular.
They are the same line.
They are not related.

They are perpendicular

Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept  form of equation is y = mx+c

where m is slope of line and c is y intercept.

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

m = -2  , c = 4

equation 2 is y = one halfx + 4 ( one half is same as 1/2)

so equation is

y = x/2 +4

comparing it with y = mx + c

m = 1/2  , c = 4

Now lets evaluate options

They are parallel.  wrong option

For lines to be parallel slope should be same.

But here slope are different -2 and 1/2 .

Thus lines are not parallel.

They are perpendicular.  correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are  perpendicular

They are the same line.  wrong option

For lines to be same both slope and y intercept should  be same.

Y intercept is same but the slopes are different -2 and 1/2  .

Thus lines are not  the same line.

They are not related.       wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

answer: i'm not sure

step-by-step explanation:

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,