algbera 2 homework problem! equation of the line

Question

1) find the equation of a line containing points (-2,8) and (3,5)

2) write an equation of the line parallel  to y=3x-2 through (1,-3)

3) write an equation of the line perpendicular  to x+y=-3 through (0,4)

Answer 1

1)

Given points are (-2,8) and (3,5)

Let A = (-2,8) = (x1,y1) and B = (3,5) = (x2,y2)

Slope (m) = (y2-y1)/(x2-x1)

               = (5-8)/(3-(-2))

               = -3/3+2

          m = -3/5

The equation of line having slope m and point (x2,y2) is y - y2 = m(x - x2)

Substitute x2= 3 , y2 = 5 and m = -3 / 5

                                                                                                       y - 5 = -3 / 5(x - 3)

                                                                                                       5y - 25 = -3x + 9

                                                                                                         5y + 3x = 34

                                                                                                          3x + 5y = 34.