Question 1076696: Write the point-slope form of the equation of the line described.
through: (-3, 2), parallel to y = -2/5x-2
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! Start with y=mx+b
"Parallel to y=-2/5x-2 " —> m=-2/5
Now we have
y = -(2/5)x + b
and just need to solve for b. Make use of the info that the line passes through (-3,2):
2 = -(2/5)(-3) + b
2 - 6/5 = b
10/5 - 6/5 = b —> b=4/5
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Ans: 
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Check: when x=-3, y = -(2/5)(-3) + 4/5 = 6/5+4/5 =10/5 = 2 (ok)
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I noticed the problem asked for "point-slope" form, I mistakenly used "slope-intercept" form. While both methods lead to the same result, point slope goes like this:
y - y0 = m (x - x0) ( m = slope, (x0,y0) is any point on the line )
m = -2/5 (b/c the line is parallel to -2/5x - 2)
and we are given the point (-3,2) on the line, so:
y-2 = (-2/5)(x-(-3))
 <<< point-slope form
Hardly any one leaves the answer in this form (but your teacher may want to see it so they know you understand the form). Most of the time that would be rearranged so the y is by itself (i.e. slope intercept form):
y = (-2/5)(x+3) + 2
y = (-2/5)x - 6/5 + 10/5
y = (-2/5)x + 4/5 ( exactly as before )
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