Question

Write an equation in standard form of the line passing through the points (3,3) and (-3,5)

Answer 1

The equation of line AB with points (3,3) and (-3,5) is given as

: x + 3y = 12

Explanation:

Here, the given points are A (3, 3) and B (-3,5).

Now, slope of any line is given as :

`m = (y_2 - y_1)/(x_2 - x_1)`

or,
`m = (5-3)/(-3 - 3)   = (2)/(-6)  = -(1)/(3)`

Hence, the slope of the line AB is (-1/3)

Now , A POINT SLOPE FORM of an equation is

(y - y0) = m (x - x0) ; (x0, y0) is any arbitrary point on line.

So, for the point (3,3) the equation of the line is

y - 3
`y-3 = -(1)/(3) (x-3)   \implies 3y - 9 = 3 -x`

Hence, the equation of line AB with points (3,3) and (-3,5) is given as:

x + 3y = 12