Help on algebra equations!!!!?

Question

so the problem is a line passes through (2,3) and (5,7), find the equation and its intercepts. thanks!

Answer 1

The slope of the line through (2,3) and (5,7) is

                        Let  (x1,y1) = (2,3) and   (x2,y2) = (5,7)

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

                                 m =  (7-3) /(5 -2)

                                 m =   4/3

Now th line equation contains slope m= 4/3 and passes through (2,3)

                                (y -y1) = m(x -x1)

                                ( y -3) = 4/3 (x - 2)

                                 3y -9 =4x - 8

                                 4x - 3y + 1= 0

The line equation passes through (2,3) and (5,7) is 4x - 3y + 1= 0

We get  x intercept by replacing  y = 0

                                 4x - 3(0)+ 1= 0

                                   4x = -1

                                     x = -1/4

We get  y intercept by replacing  x = 0

                                4(0) - 3y + 1= 0

                                  -3y = -1

                                      y = 1/3

The x and y intercepts are  -1/4, 1/3 respectively