Question

A. Find a slope-intercept equation for line A. b. Find a point-slope for line B.

Answer 1

The slope intercept form of the line is given by:
 $y = mx + b$
 The point-slope form is given by:
 $y-yo = m (x-xo)$
 Where,
 m: slope of the line
 b: cutting point with the y axis
 (xo, yo): ordered pair that belongs to the line

  For line A:
 The slope is 
 $m = \frac{1-3}{4-1}$
 $m = \frac{-2}{3}$
 The cut point with the y axis is:
 $b = \frac{11}{3}$
 Substituting values we have:
 $y = -\frac{2}{3}x + \frac{11}{3}$

  For line B:
  The slope is given by:
  $m=\frac{1-(-5)}{4-0}$
  $m=\frac{1+5}{4}$
  $m=\frac{6}{4}$
  $m=\frac{3}{2}$
  Then, the equation of the line is:
  $y-1= \frac{3}{2}(x-4)$

  Answer:
  Option A