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:

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step-by-step explanation: