Find the equation of the line passing through the point ( 2, −3) which is parallel to the line with equation y + 4x = 7

First we rearrange the equation

y + 4x = 7     to      y = −4x + 7

So we can see that the gradient of this equation is −4.

Since the line we are looking for is parallel, it must have the same gradient, −4.

So now we know we have a line for equation:

y = −4x + m

which passes through the point ( 2, −3).

We can set the values into the equation to find m:

−3 = −4 x 2 + m

−3 = −8 + m               

Now we add 8 to both sides

5 = m

So we see that the value of m is 5 and the equation we are looking for is:

y = −4x + 5