# How do you write an equation of a line containing (2,4) and parallel to x-2y=5?

Apr 22, 2018

See explanation below
$y$=0.5$x$+3

#### Explanation:

If a line is parallel to another line it must have the same gradient (co-efficient of $x$)
Re-arrange the given equation of the line into the form $y$=$m$$x$+$c$
$x$-2$y$=5
-2$y$=5-$x$
$y$=-2.5+0.5$x$
General equation of line that passes through (2,4)
y=0.5$x$+$c$
Substitute the $x$ and $y$ coordinate
4=0.5(2)+$c$
4=1+$c$
$c$=3
$y$=0.5$x$+3 (Equation of the parallel line)

I hope this helped

Apr 22, 2018

$y = \frac{1}{2} x + 3$

#### 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

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

$\text{rearrange "x-2y=5" into this form}$

$- 2 y = - x + 5$

$\text{divide all terms by } - 2$

$\Rightarrow y = \frac{1}{2} x - \frac{5}{2} \leftarrow \textcolor{b l u e}{\text{in slope-intercept form}}$

$\text{with slope m } = \frac{1}{2}$

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

$\text{to find b substitute "(2,4)" into the partial equation}$

$4 = 1 + b \Rightarrow b = 4 - 1 = 3$

$\Rightarrow y = \frac{1}{2} x + 3 \leftarrow \textcolor{red}{\text{equation of parallel line}}$

Apr 22, 2018

$2 y - x = 6$

#### Explanation:

$x - 2 y = 5$

$- 2 y = - x + 5$

$y = \left(- \frac{x}{-} 2\right) + \left(\frac{5}{-} 2\right)$

$y = \left(\frac{1}{2}\right) x - \frac{5}{2}$

Slope $m = \left(\frac{1}{2}\right)$

Equation of line parallel to given line and passing through (2,4) is

$\left(y - 4\right) = \left(\frac{1}{2}\right) \left(x - 2\right) , \text{ using slope - point form}$

$2 y - 8 = x - 2$

$2 y - x = 6$