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.

Peter already knew the slope of the line he wanted (-1/2), but wanted to find the y-intercept. So, he filled in the values he had so that he could solve for "b", the y-intercept.

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Peter apparently didn't realize that the coordinate (0, 1) is the y-intercept, so he went to more trouble than he needed to in order to determine that b=1.

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facundo3141592 facundo3141592 · Answer 2 · 2021-10-04T12:30:19+02:00

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:

https://brainly.com/question/11064712