Question

Find the equation of the line that passes through ( 4 , 1 ) and is parallel to the line passing through ( 7 , 11 ) and ( 10 , 20 ) .

Answer 1

`y-1=3(x-4)` -----> equation into point slope form

`y=3x-11` -----> equation into slope intercept form

`3x-y=11` -----> equation in standard form

Explanation:

we know that

If two lines are parallel, then their slopes are the same

step 1

Find the slope of the line passing through ( 7 , 11 ) and ( 10 , 20 )

The slope m is equal to

`m=(20-11)/(10-7)=3`

step 2

Find the equation of the line with m=3 that passes through (4,1)

The equation of the line into point slope form is equal to

`y-y1=m(x-x1)`

substitute

`y-1=3(x-4)` -----> equation into point slope form

Convert to slope intercept form

`y=mx+b`

isolate the variable y

`y=3x-12+1`

`y=3x-11` -----> equation into slope intercept form

Convert to standard form

`Ax+By=C`

`3x-y=11` -----> equation in standard form