Peter wrote the equation 1=-1/2(0)+b to find the equation of the line that is perpendicular to line y = 2x + 3 and passes through point (0, 1). why did peter write that equation? explain.

Two lines are perpendicular if the slope of one of them is equal to the opposite of the inverse of the other line's slope.

Then if one line is:

y = a*x + b

The other line must be:

y = -(1/a)*x + c.

Now to answer the question:

He wrote that equation to find the value of b, the y-intercept.

Ok, now we know that Peter wanted to get a linear equation perpendicular to:

y = 2x + 3

And that passes through (0, 1).

So what he first does is writing the general line:

y = -(1/2)*x + b

Where he uses the opposite of the inverse of the slope.

Now, by knowing that this line passes through (0, 1), what he knows is that when we use x = 0, then we must have y = 1.

Then he replaces these values in the equation to get:

1 = (-1/2)*0 + b

And with this, he can find the value of b:

1 = 0 + b

1 = b

Then the line equation is:

y = -(1/2)*x + 1

If you want to learn more, you can read:

link

to find the perimeter of the rectangle this is the expression:

x-9+x-9+3x-4+3x-4=138

if we simplify it:

8x-26=138

remember, 138 is what it all adds up to

the length is 11.5cm

the width is 57.5cm

the area is 661.25cm^2

the answers might not be correct use at own risk