What is the point slope equation of line that passes through the point (2,-3) and has the same y intercept as y =5×+2

y + 3 = (-5/2)(x - 2)

Step-by-step explanation:

First look at y =5x + 2.  It's immediately apparent that the y-intercept is 2, or (0, 2).  (0, 2) must then be a point on the new line, and we are told that (2, -3) is also on this new line.

The general point-slope equation is y - k = m(x - h).

We need to determine the slope of the new line.

Let h = 2, k = -3, x = 0 and y = 2.  Then:

2 + 3 = m(0 - 2).  Therefore, -2m = 5, and m = -5/2.

Then the equation of the new line, in point-slope form, is

y + 3 = (-5/2)(x - 2)

Let's check this result.  Do the coordinates of the y-intercept, (0, 2) satisfy this equation?

Is 2 + 3 = (-5/2)(0 - 2) true?

Is 5       = (-5/2)(-2) true?  YES