Question

Which equation is a point-slope form of the equation of this line?

a) -2x+ y + 5 = 0
b ) y = 2x - 5
c) ( y + 1 ) = - 1/2 ( x - 2 )
d) ( y - 1 ) = 2 ( x + 2 )

Answer 1

c) ( y + 1 ) = - 1/2 ( x - 2 )

1. Find the slope (m) using Y2-Y1/X2-X1
2. Use the formula: Y-Y1=M(X-X1)
3. Plug in for Y1, M, and X1

Answer 2

The first thing you should do in this case is to write the equation in its generic form.
 We have then:
 y-yo = m (x-xo)
 We look for the slope:
 m = (y2-y1) / (x2-x1)
 m = (7-1) / (1 - (- 2))
 m = 6/3
 m = 2
 We choose any point of the line:
 (xo, yo) = (1, 7)
 We substitute the values in the generic equation:
 y-7 = 2 (x-1)
 We rewrite:
 y = 2x + 5
 Equivalently:
 (y - 1) = 2 (x + 2)
 Answer: 
 d) (y - 1) = 2 (x + 2)