Question

MATH HW..... good answers only!!!

Answer 1

◆ STRAIGHT LINES ◆

$a(1,1) = (x1,y1) \\ b(2,4) = (x2,y2) \\ c(4,2) = (x3,y3) \\ \\ slope \: of \: line \: = \frac{(y2 - y1)}{(x2 - x1)} \\ \\ slope \: of \: line \: ab \: = \frac{(4 - 1)}{(2 - 1)} \\ slope \: of \: line \: ab = 3 \\ \\ now \: ,for \: 2nd \: part \: , \\ \: \\ equation \: of \: line \: of \: slope \: m \: \\ passing \: through \: (h,k) \: is \: , \\ \\( y - k) = m(x - h) \\ \\ therefore \\ \: y - 2 = 3(x - 4) \\ \\ y - 2 = 3x - 12 \\ \\ 3x - y - 10 = 0 \: \: \: \: \: ans.$

Answer 2

Part I:
  Slope is (change in y)/(change in x), often represented using the letter m.
  m = (4 -1)/(2 -1) = 3/1 = 3

The slope of AB is 3.


Part II:
  The point-slope form of the equation of a line with slope m through point (h, k) is usually written
  y -k = m(x -h)
  Adding k, you can rearrange this to
  y = m(x -h) +k
  For m = 3 and (h, k) = (4, 2) we can fill in the numbers as
  y = 3(x -4) +2
  Eliminating parentheses puts this in slope-intercept form.
  y = 3x -10 . . . equation for line p