Question

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

Answer 1

Equation of line CD is `color(brown)(y = (5/6)x - 15/2`

Explanation:

Equation of a line given two coordinates on the line is given by the formula

`(y - y_1)/ (y_2 - y_1) = (x - x_1) / (x_2 - x_1)`

Given `C (3, -5), D(6, 0)`

Hence, the equation is `(y - y_c) / (y_d - y_c) = (x - x_c) / (x_d - x_c)`

`(y + 5) / (0 + 5) = (x - 3) / (6 - 3)`

`(y + 5) / 5 = (x - 3) / 6`

`6(y + 5) = 5 (x - 3)` cross multiplying.

`6y + 30 = 5x - 15` Removing braces.

`6y = 5x - 15 - 30`

`6y = 5x - 45`

`y = (5(x - 9)) /6`

Equation of line CD is

`color(brown)(y = (5/6)x - 15/2` in the standard form `color(blue)(y = mx + c`