Convert the following equation -3x+7y =-35 from standard form to point slope form

y - 5 = (3/7)(x - 0)

Step-by-step explanation:

Determine the slope of the line -3x+7y =-35.  Solve this equation for y, obtaining 7y = 3x - 35 and then y = (3/7)x - 5.  The slope is (3/7).

The point-slope form is y - k = m(x - h), and here m = 3/7.

So we now have to find an equation in the form y - k = (3/7)(x - h).  (h, k) is the point in question:  (h, k), and k = the y-coordinate of some point can be found by using the given line -3x+7y =-35.  Supposing that we choose x = 0, then 7y = 35, and y = 5, and so one point on the line -3x+7y =-35 is (0, 5).

Substitute 0 for h and 5 for k in y - k = (3/7)(x - h).  We get

y - 5 = (3/7)(x - 0), or just

y - 5 = (3/7)(x - 0) (which is in point-slope form)