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
