Answer:
2) y = -8/3x +5
Step-by-step explanation:
For lines through a point, the point-slope form of the equation for a line is useful. It is often written as ...
y -k = m(x -h) . . . . . . line of slope m through point (h, k)
I prefer the form with k added:
y = m(x -h) +k
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Parallel lines have the same slope. In the slope-intercept form of the equation, that slope is the coefficient of x.
2) line through (3, -3) with slope -8/3:
y = (-8/3)(x -3) -3
y = -8/3x +8 -3 . . . . . . eliminate parentheses
y = -8/3x +5 . . . . . . . . simplify to slope-intercept form
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Alternate solution
You want the final form to be ...
y = mx + b
You know values for y, m, x, so you can substitute those to find the value for b.
-3 = -8/3(3) +b . . . . for (x, y) = (3, -3) and m = -8/3
-3 = -8 +b . . . . . . . . multiply
5 = b . . . . . . . . . . . . add 8
So, your equation is ...
y = -8/3x +5
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Since you're looking for a parallel line through a point (x, y) in every case, you can solve the above generic equation for b:
b = y - mx
You can read the slope from the given equation, so this can simplify finding the answers.
3) b = 1 - (-1)(3) = 4 ⇒ y = -x +4
4) b = 0 - (-7/3)(-5) = -35/3 ⇒ y = -7/3x -35/3
5) b = 0 - (7/4)(5) = -35/4 ⇒ y = 7/4x -35/4
6) ... you get the idea
