3.03 Graphs of inequalities in two variables
Interactive practice questions
Two available entertainment options for the school holidays are movies and ice-skating, with costs shown below.
The inequality $12m+20s\le150$12m+20s≤150 represents the total amount of money you can spend between the two activities.
- Movies, $m$m, which cost $\$12$$12 each
- Ice-skating, $s$s, which costs $\$20$$20 per session
What does the point $\left(0,0\right)$(0,0) represent for this inequality?
The point $\left(0,0\right)$(0,0) represents the situation where you attended only ice-skating sessions.
The point $\left(0,0\right)$(0,0) represents the situation where you attended only movies.
The point $\left(0,0\right)$(0,0) represents no money spent on movies or ice-skating sessions.
The point $\left(0,0\right)$(0,0) represents that you spent all of your budget on movies and ice-skating sessions.
True or false?
"The point $\left(0,0\right)$(0,0) lies in the solution region of the inequality $x+y>0$x+y>0."
True or false?
"If an inequality has $<$< or $>$> symbol, the graph of the inequality will have a dashed line."
True or false?
"The inequalities $3x-2y>6$3x−2y>6 and $3x-2y\ge6$3x−2y≥6 will have the same graph."