The equation of line ab is y = -1/4 x - 2. write an equation of a line parallel to line ab in slope intercept form that contains point (-3,2)

The general equation of a straight line is in the form of;
Y=MX + c,
Where m is the gradient and
C the y-intersept.
Parallel line have the same gradient.
From the equation,
Y=-1/4X - 2,
Gradient = - 1/4.

Now assuming that the second line passes through (x,y) and (-3,2).
(Y-2)/(X--3) =-1/4
4(Y-2)=-1(X+3)
4Y-8 = -X-3
4Y = -X -3+8
4Y = -X +5
Y = -1/4X +5/4

y = -(1/4)x + 5/4

Explanation:

1) Parallel lines have equal slopes.

2) The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.

3) Hence, the slope of the given equation, i.e. y = (-1/4)x - 2 is m = -1/4

4) Therefore, that is the same slope of any line parallel to it, m = -1/4

5) The slope-point equation of the line is:

y - y₁ = m (x - x₁)

6) Now you replace -1/4 for m, and the point (-3,2)

⇒ y - 2 = [ -1/4) (x - (-3) ]

7) Expand the product and simplify:

y - 2 = -x/4 - 3/4
y = -x/4 -3/4 + 2
y = -x/4 + 5/4

And that is the equation requested