Question #7580f

May 30, 2017

Let's first rewrite into $y = m x + b$ form:

Explanation:

$y = + x - 3$
$y = - x + 8$

One thing is for sure: they are not parallel (slopes of +1 and -1).

Let's see if they intersect:
$x - 3 = - x + 8 \to$
$x$'s to one side, numbers to the other (add $x + 3$ on both sides):
$x - \cancel{3} + x + \cancel{3} = - \cancel{x} + 8 + \cancel{x} + 3 \to$
$2 x = 11 \to x = 5 \frac{1}{2} \to y = x - 3 = 2 \frac{1}{2}$

They intersect in $\left(5 \frac{1}{2} , 2 \frac{1}{2}\right)$ and because the slopes multiply to $- 1$, this is a right-angle intersection.