Answer
$y=-2x+10$
Work Step by Step
The slope-intercept equation of the line has form $y=ax+b.$ The line contains the point $(5,0)$ and is parallel to the line $2x+y=8$.
Let's rewrite the last one in slope-intercept form:
$y=-2x+8.$
Two lines are parallel to each other if they have the same slope. Therefore $a=-2$. Hence $y=-2x+b$.
Let's use the condition with the point in order to determine $b$.
$0=-2\cdot 5+b\Rightarrow b=10$
Our line's equation is:
$$y=-2x+10$$
