Answer:
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
