Question

use the drawing tool(s) to form the correct answer on the provided graph.
a tire warehouse has an inventory of 100 tires. customers can only purchase tires in complete sets of four.
create and graph the solution set to the equation for the remaining amount of tires, y, in terms of the number of sets of tires purchased, x.
(chart and drawing tools interface description omitted as per instruction)

Explanation:

Step1: Formulate the equation

The initial inventory is 100 tires. Each set purchased (x) has 4 tires, so the remaining tires \( y = 100 - 4x \). The domain of \( x \) is non - negative integers such that \( y\geq0 \), so \( 100 - 4x\geq0\Rightarrow x\leq25 \), and \( x\geq0 \).

Step2: Find key points

• When \( x = 0 \), \( y=100 - 4(0)=100 \). So the point is \( (0,100) \).
• When \( x = 25 \), \( y = 100-4(25)=0 \). So the point is \( (25,0) \).
• We can also find other points, for example, when \( x = 5 \), \( y=100 - 4(5)=100 - 20 = 80 \), point \( (5,80) \); when \( x = 10 \), \( y=100 - 4(10)=60 \), point \( (10,60) \); when \( x = 15 \), \( y=100 - 4(15)=100 - 60 = 40 \), point \( (15,40) \); when \( x = 20 \), \( y=100 - 4(20)=100 - 80 = 20 \), point \( (20,20) \).

To graph the solution set, we plot these points (since \( x \) represents the number of sets of tires purchased, it should be a non - negative integer, but for the graph, we can draw a line segment connecting \( (0,100) \) and \( (25,0) \) (or plot the discrete points) as the relationship is linear.

Answer:

The equation is \( y = 100 - 4x \) with \( 0\leq x\leq25 \) (x is an integer). The graph is a line segment (or a set of discrete points) connecting \( (0,100) \) and \( (25,0) \) (and other intermediate points like \( (5,80) \), \( (10,60) \), \( (15,40) \), \( (20,20) \)) on the provided coordinate system.