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)?

We know,
If there are two equations of line like
`a_1x + b_1y + c_1 = 0` and `a_2x + b_2x + c_2 = 0` ;

then, the condition of they being parallel is

`a_1/a_2 = b_1/b_2 != c_1/c_2`

First Convert the line equation to the general form `ax + by + c = 0`

Therefore, `x - 2y = 6`

`rArr x - 2y - 6 = 0` ..........................(i)

Then, the equation of parallel line will be

`x - 2y + 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 - 2y + k = 0`
`rArr (-5) - 2(2) +k = 0`
`rArr -5 - 4 + k = 0`
`rArr k = 9`

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

The equation, at slope-intercept form is

`x - 2y + 9 = 0`
`rArr -2y = -x - 9`
`rArr 2y = x + 9`
`rArr y = 1/2 x + 9/2`, where the slope is `m = 1/2` and the y-intercept is `c = 9/2`.

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

`• " parallel lines have equal slopes"`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"rearrange "x-2y=6" into this form"`

`rArry=1/2x-3larr" with "m=1/2`

`rArry=1/2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-5,2)" into the partial equation"`

`2=-5/2+brArrb=9/2`

`rArry=1/2x+9/2larrcolor(red)"in slope-intercept form"`