Answer
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
Work Step by Step
The given line can be graphed using the x and y-intercepts.
RECALL:
(1) The x-intercept can be found by setting $y=0$ then solving for $x$.
(2) The y-intercept can be found by setting $x=0$ then solving for $y$.
Find the x-intercept of the given equation. Set $y=0$ then solve for $x$ to obtain:
\begin{array}{ccc}
\\&2x+5y&=&10
\\&2x+5(0)&=&10
\\&2x&=&10
\\&\frac{2x}{2}&=&\frac{10}{2}
\\&x&=&5
\end{array}
The x-intercept is $(5, 0)$.
Find the x-intercept of the given equation. Set $x=0$ then solve for $y$ to obtain:
\begin{array}{ccc}
\\&2x+5y&=&10
\\&2(0)+5y&=&10
\\&5y&=&10
\\&\frac{5y}{5}&=&\frac{10}{5}
\\&y&=&2
\end{array}
The y-intercept is $(0, 2)$.
Graph the line by plotting the intercepts and connecting them using a line.
(Refer to the graph in the answer part above.)
The graph covers all x-values therefore the domain is $(-\infty, +\infty)$.
The graph covers all y-values therefore the range is $(-\infty, +\infty)$.
