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`

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)=(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))=(0-(-5))/(6-3)(x-6)\\\\\Righarrow\ y=(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