# Question #6b72f

Jan 24, 2018

The equation of a straight line divides the plane into two halves

#### Explanation:

Let's first consider the equality:

$2 x + 5 y = 15$

This is the equation of a straight line, as follows:

$5 y = - 2 x + 15$, or in a more canonical form:

$y = - \frac{2}{5} x + 3$

That is, the straight line with slope $- \frac{2}{5}$ and $y$ intercept $3$.

If you take $a n y$ point $\left({x}_{1} , {y}_{1}\right)$ on that line, ${y}_{1} = - \frac{2}{5} {x}_{1} + 3$

So $a n y$ point $\left(x , y\right)$ $b e l o w$ that line satisfies $y < - \frac{2}{5} x + 3$, or equivalently:

$2 x + 5 y < 15$

That is, the solution is the half-plane $b e l o w$ the straight line $y = - \frac{2}{5} x + 3$