Answer
a) $x+y \leq5000$
b) Please see the graph, made using graphing software.
c) The cost of a ceremony is not negative, and the cost of a reception is not negative. For these reasons, the grid shows only quadrant I.
Work Step by Step
a)
wedding ceremony is $x$
reception is $y$
max budget of 5000 dollars
$x+y \leq5000$
b)
To graph the inequality, we need to have the $\leq$ sign be replaced with an $=$ sign.
Let $x=0$ (y-intercept)
$x+y =5000$
$0+y =5000$
$y=5000$
Let $y=0$ (x-intercept)
$x+y =5000$
$x+0=5000$
$x=5000$
$(0,5000)$ and $(5000,0)$ are on the line.
Use $(0,0)$ to determine what side of the line to shade.
$x+y \leq5000$
$0+0 \leq5000$
$0 \leq 5000$ is true, so we shade the side of the line with $(0,0)$.