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`

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=(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)=(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)