How do you write y - 7 = 4(x + 4) in standard form?

May 29, 2018

$4 x - y = - 23$

Explanation:

$y - 7 = 4 \left(x + 4\right)$

This is in the format of $y - {y}_{1} = m \left(x - {x}_{1}\right)$ which is known as the point-slope form. To change this to standard form ($A x + B y = C$), you need to find the values of the points $\left({x}_{1} , {y}_{1}\right)$ and the slope ($m$):

$y - 7 = 4 \left(x + 4\right)$
$y - {y}_{1} = m \left(x - {x}_{1}\right)$

Therefore,

$\left({x}_{1} , {y}_{1}\right) = \left(- 4 , 7\right)$ and $m = 4$

$y - 7 = 4 \left(x + 4\right)$

Now simplify and rearrange to get $x$ and $y$ terms on one side and constants on the other side of equal sign:

$y - 7 = 4 \left(x + 4\right)$
$y - 7 = 4 x + 16$
$y = 4 x + 16 + 7$
$y = 4 x + 23$
$- 4 x + y = 23$

This is almost in the format of $A x + B y = C$ but $A x$ cannot have a negative sign in front of it. To get rid of this negative, divide both sides of the equation by $- 1$:

$\frac{- 4 x + y}{-} 1 = \frac{23}{-} 1$
$4 x - y = - 23$

Now the equation is in standard form because $A = 4$, $B = - 1$ and $C = - 23$.