Answer:
Inequality is [tex]4x+3y\leq 87[/tex]
Slope intercept form is [tex]y\leq 29-\frac{4}{3}x[/tex]
Solutions are [tex](2,3)\,,\,(3,4)[/tex]
Graph: attached to the question
Step-by-step explanation:
Given: Group dance numbers last 4 minutes and a solo performance lasts 3 minutes. The maximum duration for the recital is 87 minutes.
To find: inequality (in standard form) that describes the given situation, inequality in slope-intercept form, solutions for the inequality
To graph: the inequality
Solution:
x denotes the number of group dances on the program
y denotes the number of solo numbers on the program
Total duration of group dance numbers = [tex]4x[/tex] minutes
Total duration of solo performance = [tex]3y[/tex] minutes
According to question,
[tex]4x+3y\leq 87[/tex]
Slope intercept form of equation is [tex]y\leq mx+c[/tex] where m denotes slope of line and c denotes y-intercept of the line.
Slope intercept form of [tex]4x+3y\leq 87[/tex] :
[tex]4x+3y\leq 87\\3y\leq 87-4x\\y\leq 29-\frac{4}{3}x[/tex]
For [tex](x,y)=(2,3)[/tex],
[tex]4(2)+3(3)\leq 87\\8+9\leq 87\\17\leq 87\,\,which\,\,is\,\,true[/tex]
So, [tex](2,3)[/tex] is a solution of the inequality.
For [tex](x,y)=(3,4)[/tex],
[tex]4(3)+3(4)\leq 87\\12+12\leq 87\\24\leq 87\,\,which\,\,is\,\,true[/tex]
So, [tex](3,4)[/tex] is a solution of the inequality.
Graph: attached as image
