Can anyone me? i started working on the 2nd one, but got stuck instantly

  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

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

first

Step-by-step explanation: