1.Write an equation of the line that passes through point P and is parallel to the line with the given equation P(2,6); Y= 2x +1

I got Y= 2x +2

2. Write an equation of the line that passes through point P and is parallel to the line with the given equation P(-1,3); Y= -4x +7
I got Y= -4x -1

Thanks

1. To find the equation of a line that is parallel to another line, we need to use the slope of the given line. The slope of a line is represented by the coefficient of x in the equation of the line.

In the given equation Y = 2x + 1, the coefficient of x is 2, which represents the slope of the line.

Since we want to find a line that is parallel to this given line and passes through point P(2,6), we know that the slope of the parallel line will also be 2.

Now, we can use the point-slope form of the equation of a line, which is: y - y1 = m(x - x1), where m represents the slope and (x1, y1) represents the coordinates of the given point.

Plugging in the values, we get:
y - 6 = 2(x - 2)

Expanding and simplifying the equation, we get:
y - 6 = 2x - 4
y = 2x + 2

So, the correct equation of the line that passes through point P(2,6) and is parallel to the given line Y = 2x + 1 is y = 2x + 2.

2. Similarly, to find the equation of a line that is parallel to the given line Y = -4x + 7, we need to use the slope of the given line.

In the given equation Y = -4x + 7, the coefficient of x is -4, which represents the slope of the line.

Since we want to find a line that is parallel to this given line and passes through point P(-1,3), we know that the slope of the parallel line will also be -4.

Using the point-slope form again, we get:
y - 3 = -4(x - (-1))

Simplifying the equation, we get:
y - 3 = -4x - 4
y = -4x - 1

So, the correct equation of the line that passes through point P(-1,3) and is parallel to the given line Y = -4x + 7 is y = -4x - 1.

P(2,6); Y= 2x +1

I got Y= 2x +2
-------------------------
y = 2 x + b
6 = 2*2 + b
b = 2 so agree
======================
P(-1,3); Y= -4x +7
I got Y= -4x -1
-----------------------
3 = -4 (-1) + b
b = -1
so agree again

Thank you!