Question

What is the equation of the line that goes through `( 6,3)` and is parallel to `8x-y=7`?

Answer 1

`y=8x-45`

Explanation:

`"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 "8x-y=7" into this form"`

`"add y to both sides"`

`8xcancel(-y)cancel(+y)=y+7`

`rArr8x=y+7larrcolor(blue)"subtract 7 from both sides"`

`rArry=8x-7larrcolor(blue)"in slope-intercept form"`

`"with " m=8`

`• " Parallel lines have equal slopes"`

`rArry=8x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(6,3)" into the partial equation"`

`3=48+brArrb=3-48=-45`

`rArry=8x-45larrcolor(red)"equation of parallel line"`

Answer 2

`y=8x-45`

Explanation:

First, rearrange equation to make `y` the subject.

`8x-y = 7`
`y = 8x-7`

Since the second line is parallel to `y=8x-7`, it means that it has the same gradient.

`y=8x+c`

Now put the coordinates in to find the equation of the line.

`y-3 = 8(x-6)`

`y-3 = 8x -48`

`y=8x-45`