Question

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

Answer 1

(-2,-4)(2,2)
slope = (2+4)/(2+2) = 6/4 = 3/2

the equation, in point-slope form
y - y1 = m(x - x1)

so
equation, passes through the point (−3, 1)
y - 1 = 3/2(x + 3)

answer 

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

Answer 2

(2,2)(-2,-4)
slope = (-4 - 2) / (-2 - 2) = -6 / -4 = 3/2....slope of given line is 3/2...a parallel line will have the same slope

y = mx + b
slope(m) = 3/2
(-3,1)....x = -3 and y = 1
now we sub and find b, the y int
1 = 3/2(-3) + b
1 = -9/2 + b
1 + 9/2 = b
2/2 + 9/2 = b
11/2 = b

so ur parallel equation is : y = 3/2x + 11/2