Question

Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6. Type your answer in the box provided or use the upload option to submit your solution.

Answer 1

Answer: $x-2y=-10$

Step-by-step explanation:

Write $x - 2y = 6$ in intercept form($y=mx+c$).

$2y =x- 6$

$y =dfrac{x- 6}{2}$

$y =dfrac{x}{2}-3$

Here , slope of line  $x - 2y = 6$  = $m=\dfrac{1}{2}$  (Coefficient of x)

Also , the slope of two parallel lines are equal.  

Equation of line passing through point (a,b) and has slope m is given by :_

$(y-b)=m(x-a)$

Standard form of equation : $Ax+By= C$ ,where A is  positive integer a,d B and C be any integer.

Equation of the line parallel to line  $x - 2y = 6$  and passing through (-2, 4)  will be :-

$(y-4)=\dfrac{1}{2}(x-(-2))\\\\ 2(y-4)=(x+2)\\\\ 2y-2(4)=x+2\\\\2y-8=x+2\\\\ x-2y=-8-2\\\\ x-2y=-10\ \ {\text{(Standard form)}}$  

Answer 2

Rewrite the equation: 2y=x-6, y=x/2-3, so slope is 1/2 which is also the slope of the parallel line.
It will have the equation y=x/2+a where a is found by plugging in the given point: 4=-1+a, so a=5.
Therefore y=x/2+5. (This can also be written 2y=x+10 or x-2y+10=0)