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:
$\frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1}$
From the given data, we have that
$y2 = - 3 \\ y1 = 3 \\ x2 = 5 \\ x1 = 0$
Therefore, substitute in the given values:
We have that:
$\frac{y - (3)}{x - (0)} = \frac{( - 3) - (3)}{(5) - (0)}$
Simplify further
$\frac{y - 3}{x} = \frac{ - 6}{5}$
Multiply both sides by the LCM, 5x:
$5x( \frac{y - 3}{ x} ) = 5x( \frac{ - 6}{5} )$
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