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