# How do you write a slope-intercept equation for a line parallel to the line x-2y=6 which passes through the point (-5,2)?

Dec 19, 2017

$y = \frac{1}{2} x + \frac{9}{2}$

#### Explanation:

We know,
If there are two equations of line like
${a}_{1} x + {b}_{1} y + {c}_{1} = 0$ and ${a}_{2} x + {b}_{2} x + {c}_{2} = 0$ ;

then, the condition of they being parallel is

${a}_{1} / {a}_{2} = {b}_{1} / {b}_{2} \ne {c}_{1} / {c}_{2}$

First Convert the line equation to the general form $a x + b y + c = 0$

Therefore, $x - 2 y = 6$

$\Rightarrow x - 2 y - 6 = 0$ ..........................(i)

Then, the equation of parallel line will be

$x - 2 y + k = 0$ ........................................(ii) (k can be any constant)

If it passes through the point (-5, 2), then the equation will be satisfied with these values.

Lets put $x = - 5$ and $y = 2$ in eq(ii).

Therefore, $x - 2 y + k = 0$
$\Rightarrow \left(- 5\right) - 2 \left(2\right) + k = 0$
$\Rightarrow - 5 - 4 + k = 0$
$\Rightarrow k = 9$

Then the required equation will be $x - 2 y + 9 = 0$.

The equation, at slope-intercept form is

$x - 2 y + 9 = 0$
$\Rightarrow - 2 y = - x - 9$
$\Rightarrow 2 y = x + 9$
$\Rightarrow y = \frac{1}{2} x + \frac{9}{2}$, where the slope is $m = \frac{1}{2}$ and the y-intercept is $c = \frac{9}{2}$.

graph{y = (x + 9)/2 [-20.27, 20.26, -10.14, 10.13]}

Dec 19, 2017

$y = \frac{1}{2} x + \frac{9}{2}$

#### Explanation:

• " parallel lines have equal slopes"

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

•color(white)(x)y=mx+b

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

$\text{rearrange "x-2y=6" into this form}$

$\Rightarrow y = \frac{1}{2} x - 3 \leftarrow \text{ with } m = \frac{1}{2}$

$\Rightarrow y = \frac{1}{2} x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute "(-5,2)" into the partial equation}$

$2 = - \frac{5}{2} + b \Rightarrow b = \frac{9}{2}$

$\Rightarrow y = \frac{1}{2} x + \frac{9}{2} \leftarrow \textcolor{red}{\text{in slope-intercept form}}$