Question

The line that passes through (-2, 4) and is parallel to x - 2y= 6

Answer 1

The equation of other line parallel to given line is y =
`(x)/(2)` + 5 .

Explanation:

Given as :

The equation of a line is

x - 2 y = 6

Or, 2 y = x - 6

Or, y =
`(1)/(2)`x -
`(6)/(2)`

i.e y =
`(1)/(2)`x - 3

The standard equation of line is given as

y = m x + c

where m is the slope of line

Now, comparing given line with standard line equation

The slope of line x - 2 y = 6 is m =
`(1)/(2)`

Again

Other line is passing through point (- 2 , 4) and is parallel to given line

For parallel line condition

slope of both lines are equal

Let The slope of other line = M

So, M = m =
`(1)/(2)`

Again

Equation of line with slope
`(1)/(2)` and passing through point (-2 , 4)

y -
`y_1` = M ( x -
`x_1` )

i.e y - 4 = (
`(1)/(2)`) ( x + 2)

Or, y - 4 =
`(x)/(2)` + 1

Or, y =
`(x)/(2)` + 1 + 4

i.e y =
`(x)/(2)` + 5

Hence, The equation of other line parallel to given line is y =
`(x)/(2)` + 5 . Answer