Answer :
Considering the definition of an inequality, the inequality in slope intercept form is y < 1,000- 2x.
Definition of inequality
An inequality is the existing inequality between two algebraic expressions, connected through the signs:
- greater than >.
- less than <.
- less than or equal to ≤.
- greater than or equal to ≥.
An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Slope intercept form
A linear equation o line can be expressed in the slope intercept form y=mx + b.
where
- x and y are coordinates of a point.
- m is the slope.
- b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.
Inequality in this case
In this case, you know that a movie theater makes a profit of:
- $10 on adult tickets.
- $5 for children's tickets.
- the profit is less than $5,000.
Considering that:
- x is the number of adult ticket sold.
- y is the number of children ticket sold.
- P is the amount of profit made by selling "x" adult tickets and "y" children tickets.
you have that the inequality that expresses the profit is
10x + 5y < 5,000
The inequality in slope intercept form is expressed as:
5y < 5,000 - 10x
y < (5,000 - 10x)÷ 5
y < 5,000÷ 5 - 10÷ 5x
y < 1,000- 2x
Finally, the inequality in slope intercept form is y < 1,000- 2x.
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