The correct graph option is [tex]\boxed{\bf option 2}[/tex].
Further explanation:
Given:
The number of apples in the bag is [tex]x[/tex].
The weight of each apple is [tex]\frac{1}{3}\text{ pound}[/tex].
The total weight of the grocery bag is less than [tex]5\text{ pounds}[/tex].
Calculation:
The weight of [tex]x[/tex] apple is [tex]\frac{x}{3}\text{ pounds}[/tex].
The weight of the grapes is [tex]y[/tex] pound.
Write the inequality of the above equation.
[tex]\boxed{\dfrac{1}{3}x+y<5}[/tex] …… (1)
Substitute [tex]0[/tex] for [tex]y[/tex] in equation (1) to obtain the value of [tex]x[/tex] as follows:
[tex]\begin{aligned}\dfrac{x}{3}+y&<5\\\dfrac{x}{3}+0&<5\\ x&<15\\\end{aligned}[/tex]
Substitute [tex]0[/tex] for [tex]x[/tex] in equation (1) to obtain the value of [tex]y[/tex] as follows:
[tex]\begin{aligned}\dfrac{1}{3}\left(0\right)+y&<5\\0+y&<5\\ y&< 5\\\end{aligned}[/tex]
Now check the option to find the correct graph for the above inequality.
First graph shows the value of [tex]x[/tex] is greater than [tex]15[/tex] which is not correct.
Second graph shows the value of [tex]x[/tex] is less than [tex]15[/tex] and value of [tex]y[/tex] is less than [tex]5[/tex].
Third graph shows the value of [tex]x[/tex] is greater than [tex]5[/tex] which is not correct.
Fourth graph shows the value of [tex]x[/tex] is less than [tex]15[/tex] which is not correct.
Therefore, the correct option is [tex]\boxed{\bf option 2}[/tex].
Learn more:
1. Representation of graph https://brainly.com/question/2491745
2. Equation of line https://brainly.com/question/1473992
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear inequality
Keywords: Graph, inequality, apple, grapes, pound, weight, grocery, grocery bag, 5 pounds, x apples, y pounds grapes, total weight.
