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

Answer:

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

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

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

Step-by-step 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