Question

Find an equation of the line through (3,6) and parallel to y = 4x - 7.

Answer 1

`y=4x-6`

Explanation:

Okay, to do this we must understand what parallel means.

parallel means that that one line will NEVER touch the other. In order for this to happen they must be increasing (or decreasing) by the SAME rate. I.e the slope of your line must be the same as the lin in question thus our equation looks like,

`y=4x+c`.

Now lets find
`c`.

To do this, plug the point (3,6) into the equation

6=4(3)+C

6=12+C

-6=C

Thus now that we know C, our equaiton is

`y=4x-6`

Answer 2

y = 4 x - 6

Explanation:

We have to know that,

If two lines are parallel the slopes of the two lines are equal but not the y - intercept.

In the equation,

y = m x + c

m ⇒ slope

c ⇒ y - intercept.

According to the question,

the equation they have given is,

y = 4x - 7

We have already find the slope of the new line.

That is,

m = slope = 4 (because the 2 lines are parallel)

Now we have to find y - intercept.

Let us find now.

( 3 , 6 ) ⇔ ( x , y )

y = m x + c

6 = 4 × 3 + c

6 = 12 + c

6 - 12 = c

-6 = c

There fore, the equation of the new line is,

y = m x + c

y = 4 x - 6

Hope this helps you :-)

Let me know if you have any other questions :-)