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)