y-7=3(x-4)+6

Solve for y, and that will give you your equation parallel to y=3x+6. Your result equation should have the same slope as the first, 3.

Good luck!

if the first equation is y=3x+6 and the second equation is parallel to it, but passes through (4,7), then the second equation must have the same slope as the first.

So we have y=3x + b

now we need to solve for b.

putting (4,7) into the equation, we get:

7=3*4 + b

7 = 12 + b

7-12 = 12 + b – 12

-5 = b

So the equation we are looking for is

y=3x – 5

7=3(4) + b

You need to find b so isolate the variable

7-12 = 12 – 12 + b

-5= b

So

y = 3x – 5.

And for it to be parallel the base can change, but slope has to be 3x

So

y = 3x +6 would be parallel

But

y = x + 6 wouldn’t be.

m = slope

b = y – intercept

if we want a line to be parallel to another line then they have the same slope.

So we have y = 3x + b

to find b, plug in the point (4, 7) and solve for b.

7 = 3(4) + b

7 = 12 + b

-5 = b

answer: y = 3x – 5