Question

Line CD passes through points C(3, –5) and D(6, 0). What is the equation of line CD in standard form?

Answer 1

Answer: $5x-3y=30$

Step-by-step explanation:

We know that the equation a line in point-slope form passing through points (a,b) and (c,d) is given by :-

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Then , the equation a line in point-slope form passing through points C(3, –5) and D(6, 0) is given by :-

$(y-(0))=\dfrac{0-(-5)}{6-3}(x-6)\\\\\Righarrow\ y=\dfrac{5}{3}(x-6)\\\\\Rightarrow\ 3y=5x-30\\\\\Rightarrow\ 5x-3y=30$

Hence, the equation of line CD in standard form  : $5x-3y=30$

Answer 2

To answer the problem above, we can start with the formation of the point-slope form of a line. The slope is solved through,

                                    m = (y2 - y1)/(x2 - x1)
                                     m = (0 - -5)/ (6 - 3) = 5/3

The point - slope form of the equation of the line is,

                                    y - y2 = m(x - x2)

Substituting the known data, 

                                   y - 0 = (5/3)(x - 6)
This simplifies into, 

                                    y = 5x/3 - 10

Thus, the standard form of the equation is, 

                                      5x - 3y = 30