# How do you find the general form of the line with slope -2 passing through the point (-4, 6)?

Jun 27, 2018

$y = - 2 x + c$ is the general equation with a slope of -2

Now put (-4,6) into the equation to find the specific equation

$6 = - 2 \times - 4 + c$

$6 = 8 + c$

$- 2 = c$

$\implies y = - 2 x - 2$

Jun 27, 2018

$2 x + y + 2 = 0$

#### Explanation:

$\text{the equation of a line in "color(blue)"general form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{A x + B y + C = 0} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where A is a positive integer and B, C are integers}$

$\text{obtain the equation in "color(blue)"slope-intercept form}$

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{here } m = - 2$

$y = - 2 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-4,6)" into the partial equation}$

$6 = 8 + b \Rightarrow b = 6 - 8 = - 2$

$y = - 2 x - 2 \leftarrow \textcolor{red}{\text{in slope-intercept form}}$

$\text{subtract "2x-2" from both sides}$

$2 x + y + 2 = 0 \leftarrow \textcolor{red}{\text{in standard form}}$

Jun 27, 2018

$y = - 2 x - 2$

#### Explanation:

Slope is always -2 which means it is a straight line where $y$ increases by -2 for every 1 that $x$ increases.

i.e. $y$ decreases by 2 for every 1 that $x$ increases.

The general form will therefore be:

y=-2x +c (where $c$ is a constant that we don't know yet).

To find $c$ we need to know where the line crosses the Y axis
(when $x = 0$ then $y = - 2 \left(0\right) + c$, i.e. $y = c$)

The point (-4, 6) tells us that when $x$ is -4, $y$ is 6, so using these 2 values in the general form equation:
$6 = - 2 \left(- 4\right) + c$
$6 = 8 + c$
$6 - 8 = c$
c=-2

so the equation for the line is y=-2x-2

check this by putting x=-4 into the equation and seeing if y = 6:
y = -2(-4) - 2 = 8 - 2 = 6 (looks correct)