Answer
a) $30x + .15y \leq 500$
b) Please see the graph, made using graphing software
c) We cannot have a negative number of days, and we cannot have a negative number of miles. That is why the grid shows only quadrant I.
Work Step by Step
a)
500 max budget
30 dollars per day (x)
.15 dollars per mile (y)
$500 \geq 30x+.15y$
$30x + .15y \leq 500$
b)
$30x + .15y \leq 500$
Let $x=0$
$30x + .15y \leq 500$
$30*0 + .15y \leq 500$
$.15y \leq 500$
$.15y/.15 \leq 500/.15$
$y \leq 3333.33$
Let $y=0$
$30x + .15y \leq 500$
$30x + .15*0 \leq 500$
$30x \leq 500$
$30x/30 \leq 500/30$
$x \leq 16.66$
$(0, 3333.33)$ and $(16.66,0)$ are on the line.
Use $(0,0)$ to determine what side of the line to shade.
$30x + .15y \leq 500$
$30*0 + .15*0 \leq 500$
$0 + 0 \leq 500$
$0 \leq 500$ is true, so we shade the side of the line with the point $(0,0)$.