# How do you find the x and y intercepts for 5x+2y=10?

Nov 15, 2015

The $x$ intercept is$\left(2 , 0\right)$, and the $y$ intercept is $\left(0 , 5\right)$.

#### Explanation:

We need to find the points in which the line crosses each axis.

The line crosses the $x$ axis in a point of the form $\left({x}_{0} , 0\right)$. If such a point belongs to the line, then it satisfies its equation, so

$5 {x}_{0} + 2 \cdot 0 = 10 \to 5 {x}_{0} = 10 \to {x}_{0} = 2$

The line crosses the $y$ axis in a point of the form $\left(0 , {y}_{0}\right)$. If such a point belongs to the line, then it satisfies its equation, so

$5 \cdot 0 + 2 {y}_{0} = 10 \to 2 {y}_{0} = 10 \to {y}_{0} = 5$