Question
Jay wrote an equation to determine the sales tax on an item he wanted to buy. The equation was y = 0.09 x, where y represents the amount of sales tax and x represents the cost of the item before tax is added. Which graph represents this information?
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (10, 0.9).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (1, 10).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (30, 1).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (1, 30). abc or d
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (10, 0.9).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (1, 10).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (30, 1).
Sales Tax Amounts
On a coordinate plane, the x-axis is labeled Cost of Item (in dollars) and the y-axis is labeled sales tax (in dollars). A line goes through (1, 30). abc or d
Answers
GPT-4o mini
To determine which graph represents the equation \( y = 0.09x \), we need to analyze how the sales tax (y) relates to the cost of the item (x). According to the equation, the sales tax is 9% of the cost of the item.
Let's evaluate this by picking some values for \( x \) (the cost of the item):
1. If \( x = 10 \):
\[
y = 0.09 \cdot 10 = 0.9
\]
This would give us the point (10, 0.9).
2. If \( x = 1 \):
\[
y = 0.09 \cdot 1 = 0.09
\]
This would give us the point (1, 0.09).
3. If \( x = 30 \):
\[
y = 0.09 \cdot 30 = 2.7
\]
This would give us the point (30, 2.7).
4. If \( x = 100 \):
\[
y = 0.09 \cdot 100 = 9
\]
This would give us the point (100, 9).
Now, looking at the graph options provided:
1. The first graph goes through (10, 0.9), which matches our calculations for \( x = 10 \).
2. The second graph goes through (1, 10), which does not match as we calculated \( y = 0.09 \) for \( x = 1 \).
3. The third graph goes through (30, 1), which does not match since we calculated \( y = 2.7 \) for \( x = 30 \).
4. The fourth graph goes through (1, 30), which is not possible as \( y \) cannot be that high for \( x = 1 \).
Based on the above analysis, the correct graph is the first one that goes through the point (10, 0.9).
Thus, the correct answer is the first graph (Graph A).
Let's evaluate this by picking some values for \( x \) (the cost of the item):
1. If \( x = 10 \):
\[
y = 0.09 \cdot 10 = 0.9
\]
This would give us the point (10, 0.9).
2. If \( x = 1 \):
\[
y = 0.09 \cdot 1 = 0.09
\]
This would give us the point (1, 0.09).
3. If \( x = 30 \):
\[
y = 0.09 \cdot 30 = 2.7
\]
This would give us the point (30, 2.7).
4. If \( x = 100 \):
\[
y = 0.09 \cdot 100 = 9
\]
This would give us the point (100, 9).
Now, looking at the graph options provided:
1. The first graph goes through (10, 0.9), which matches our calculations for \( x = 10 \).
2. The second graph goes through (1, 10), which does not match as we calculated \( y = 0.09 \) for \( x = 1 \).
3. The third graph goes through (30, 1), which does not match since we calculated \( y = 2.7 \) for \( x = 30 \).
4. The fourth graph goes through (1, 30), which is not possible as \( y \) cannot be that high for \( x = 1 \).
Based on the above analysis, the correct graph is the first one that goes through the point (10, 0.9).
Thus, the correct answer is the first graph (Graph A).