Question

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

Answer 1

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

Answer 2

`y=1/2x+3`

Explanation:

`• " 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=5" into this form"`

`-2y=-x+5`

`"divide all terms by "-2`

`rArry=1/2x-5/2larrcolor(blue)"in slope-intercept form"`

`"with slope m "=1/2`

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

`"to find b substitute "(2,4)" into the partial equation"`

`4=1+brArrb=4-1=3`

`rArry=1/2x+3larrcolor(red)"equation of parallel line"`

Answer 3

`2y - x = 6`

Explanation:

`x-2y = 5`

`-2y = -x + 5`

`y = (-x/-2) + (5/-2)`

`y = (1/2) x - 5/2`

Slope `m = (1/2)`

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

`(y - 4) = (1/2) (x - 2), " using slope - point form"`

`2y - 8 = x - 2`

`2y - x = 6`