Which equation is an equation of the line parallel to the line through the points (-1, 4) and (-2, 1)

Answer 1

Let's use the slope intercept form where y = mx + b and m = gradient and b = y intercept.

gradient = change in y / change in x

for two parallel lines m1 = m2.

from (-1,4) to (-2, 1) the change in y is -3, and the change in x is -1. Hence gradient = -3/-1 = 3

Hence our desired equation has the form y = 3x + n where n is any number.

If we want to find the specific line through the two points, substitute to get (4) = 3(-1) + n

=> n = 7 and the line through the 2 points is y = 3x + 7

Hence, y = 3x + n where n ≠ 7 will be parallel. e.g. y = 3x + 5 or y = 3x -1

Answer 2

Let the equation of line passing through

(-1,4 )

be

y= mx+b

4 = m(-1) +b

or

4= -m+b ...... Eq1

For (-2,1)

1= m(-2) +b

1= -2m+b .... Eq 2

Solving m =

b= 7 and m =3

Equation through these two points is

y= 3m +7

A line parallel to this line will also have same slope

Thus

y= 3m+b is equation of that line