Question

What is an equation of the line that passes through the points (0,3) and (5,−3)? Put your answer in fully reduced form.

Answer 1

Using the "gradient, two-point form", we have:

`(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)`
From the given data, we have that

`y2 = - 3 \\ y1 = 3 \\ x2 = 5 \\ x1 = 0`
Therefore, substitute in the given values:
We have that:

`(y - (3))/(x - (0)) = (( - 3) - (3))/((5) - (0))`
Simplify further

`(y - 3)/(x) = ( - 6)/(5)`
Multiply both sides by the LCM, 5x:

`5x( (y - 3)/( x) ) = 5x( ( - 6)/(5) )`
Simplify:

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

`5y - 15 = - 6x`
Note that the equation of a straight line is given by Ax + By = C where A and B are coefficients of x and y respectively. C is the constant. Hence:
6x+5y=15