Tom has $10 that he wants to use to buy pens and pencils. However, he does not want to buy more pens than pencils. A pen costs $3, and a pencil costs $1. Which graph represents this scenario? (Here, x represents the number of pens and y the number of pencils.)
I think it is the second graph what do you guys think the answer is
Obviously we can't see your graph.
He can buy one or two pens.
it is i do not care
Does anyone know the answer
To solve this problem, we need to set up an inequality based on the given conditions and then graph it.
First, let's assign variables to represent the number of pens and pencils. Let's use x for the number of pens and y for the number of pencils.
According to the scenario, Tom wants to buy pens and pencils using his $10 budget but does not want to buy more pens than pencils. Based on the prices given, a pen costs $3, and a pencil costs $1.
Therefore, the cost of x pens would be 3x dollars, and the cost of y pencils would be y dollars.
Given that Tom has $10 and he wants to buy pens and pencils without exceeding his budget, we can write the inequality: 3x + y ≤ 10.
To graph this inequality, we can rewrite it in slope-intercept form as y ≤ -3x + 10.
Now, let's plot the graph:
1. Start with a coordinate plane.
2. To plot the equation y = -3x + 10, begin by plotting the y-intercept, which is the point (0,10).
3. Use the slope (-3) to find additional points. For example, if you move one unit to the right (increase x by 1), you move three units down (decrease y by 3).
4. Connect the plotted points with a straight line.
5. Finally, shade the area below the line since we are looking for y values less than or equal to (-3x + 10).
In summary, the graph that represents the scenario is a line with a negative slope that includes the y-intercept (0,10) and is shaded below the line.