Question

The line that contains the point Q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)

Answer 1

y + 2 =
`(2)/(3)`(x - 1)

Explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 4 =
`(2)/(3)`(x - 3) ← is in point- slope form

with slope m =
`(2)/(3)`

Parallel lines have equal slopes, thus equation of parallel line

with m =
`(2)/(3)` and (a, b) = Q(1, - 2) is

y - (- 2) =
`(2)/(3)`(x - 1) , that is

y + 2 =
`(2)/(3)`(x - 1)