Question

write an equation passing through the point and parallel to the given line. (4,7);y=3x+4

Answer 1

Answer:

$y=3x-5$

Step-by-step explanation:

step 1

Find the slope

we know that

If two lines are parallel, then their slopes are equal

The slope of the given line is $m=3$

so

The slope of the line parallel to the given line is also $m=3$

step 2

Find the equation of the line in point slope form

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

we have

$m=3$

$point\ (4,7)$

substitute

$y-7=3(x-4)$

step 3

Convert to slope intercept form

isolate the variable y

$y-7=3x-12\\y=3x-12+7\\y=3x-5$