Question 174662
x is greater or equal to 0
Because, 'x' represents the number of hours Unita baby-sat, it has to "equal to or greater" than zero because you can't work for "negative hours".
.
y is greater or equal to 0
Similarly, because 'y' represents the number hour Unita tutored -- it has to "equal to or greater" than zero because you can't work for "negative hours".
.
Since there are two variables -- x and y -- we'll need to find two expressions or formulas.
.
The first formula deals with the amount of money she makes:
That is, "total earned by baby-sitting" plus "total earned tutoring" has to be "greater or equal" to $65.
3x + 6y >= 65
The expression on the left side is the "total amount" Unita earned by baby-sitting and tutoring.  For example, since she gets $3 per hour for baby-sitting, the amount earned is 3 times the number of hours she baby-sat (which is 'x').  The same for 6y.
.
The second formula deals with the total number of hours Unita worked:
That is, "total hours baby-sitting" plus "total hours tutoring" has to be "less than or equal" to 15 hours.
x + y <= 15
This expression represents hours
Since her parents is allowing her to work a MAXIMUM of 15 hours, the hours worked baby-sitting plus the hours worked tutoring has be "less than or equal" to 15.
.
The graph represents these two formulas.  The first:
3x + 6y >= 65
Manipulate to "slope-intercept" form:
6y >= -3x + 65
y >= (-3/6)x + 65/6
y >= (-1/2)x + 65/6
graping this line: slope=(-1/2) and y-intercept at (0, 65/6)
Since it is >= the line is SOLID and you SHADE the area ABOVE this line.
.
The second:
x + y <= 15
Manipulate to "slope-intercept" form:
y <= -x + 15
graping this line: slope=(-1) and y-intercept at (0, 15)
Since it is <= the line is SOLID and you SHADE the area BELOW this line.
.
Where the two shaded regions OVERLAP are the possible values for x and y.
.
Write back if you still have questions.