Question

this graph shows how the time required to complete an online shopping transaction is related to the number of products being purchased. online shopping (graph with time (seconds) on y - axis from 10 to 100 and products being purchased on x - axis from 0 to 10, a line graph). if it takes 90 seconds to complete a transaction, how many products are being purchased? 6 products, 9 products, 8 products, 7 products

Explanation:

Step1: Analyze the graph's pattern

The graph is a straight line, so we can find the relationship between time (seconds) and number of products. Let's assume the equation of the line is \( y = mx + b \), where \( y \) is time, \( x \) is number of products. From the graph, when \( x = 0 \), \( y = 10 \), so \( b = 10 \). Let's find the slope \( m \). When \( x = 10 \), \( y = 100 \) (from the graph's end point). So \( m=\frac{100 - 10}{10-0}=\frac{90}{10} = 9 \). So the equation is \( y = 9x+10 \).

Step2: Solve for \( x \) when \( y = 90 \)

We substitute \( y = 90 \) into the equation \( 90=9x + 10 \). Subtract 10 from both sides: \( 90 - 10=9x \), so \( 80 = 9x \)? Wait, no, maybe my initial assumption is wrong. Wait, looking at the graph, when time is 90 seconds, let's check the x - axis. The graph line: when y (time) is 10, x=0; y=20, x=1 (since from (0,10) to (1,20)? Wait no, maybe the slope is 9? Wait, no, let's check the options. Let's look at the graph: when time is 90, what's x? Let's see the options. Let's check the graph again. The line goes from (0,10) to (10,100). So the slope is \( \frac{100 - 10}{10-0}=9 \), so the equation is \( y = 9x + 10 \). Now, if \( y = 90 \), then \( 90=9x + 10 \). Subtract 10: \( 80 = 9x \)? No, that can't be. Wait, maybe I misread the graph. Wait, the options are 6,9,8,7. Let's check the graph: when time is 90, the x - value (number of products) should be 8? No, wait, let's look at the y - axis. Wait, the y - axis is time in seconds. Let's see the grid: each square is 10 seconds? Wait, from 10 to 20 is 10 seconds, x from 0 to 1. Wait, maybe the correct way is to look at the graph: when time is 90, the x (products) is 8? No, wait the options: 9 products. Wait, let's re - examine. The graph: at x = 8, what's y? Let's see, the line: from (0,10), each product adds 9 seconds? Wait, no, maybe the slope is 9. Wait, when x = 8, y=9*8 + 10=82, no. Wait, maybe the graph is such that when y = 90, x = 8? No, wait the options: 9 products. Wait, let's check the graph again. The end point is (10,100). So when y = 90, x is 8? No, 100 - 10 = 90, so from x=0 to x=10, y goes from 10 to 100. So the difference in y is 90, difference in x is 10. So per product, the time increases by 9 seconds (90/10). So starting from 10 seconds at 0 products. So for y = 90, the increase from 10 is 80? No, 90 - 10 = 80. 80/9 is not integer. Wait, maybe the graph is simpler. Let's look at the options. Let's check each option:

- For 6 products: Let's see the time. If x=6, y=9*6 + 10=64, not 90.
- For 9 products: y=9*9 + 10=91, close to 90? Wait, maybe my equation is wrong. Wait, maybe the y - intercept is 10, and the slope is 9. Wait, when x=8, y=9*8 + 10=82. x=9, y=9*9+10=91. x=7, y=9*7 + 10=73. x=6, y=64. But the option is 8,9,7,6. Wait, maybe the graph is drawn such that when time is 90, the number of products is 8? No, wait the correct answer should be 8? No, wait the graph's line: when y=90, looking at the x - axis, the point on the line where y=90 is at x=8? Wait, no, maybe I made a mistake. Wait, let's look at the graph again. The y - axis: 10,20,30,...100. The x - axis: 0 - 10. The line goes from (0,10) to (10,100). So the equation is y=9x + 10. So when y=90, 9x=80, x=8.88..., but the options are 6,9,8,7. Wait, maybe the graph is not linear with slope 9. Wait, maybe the slope is 10? Wait, if slope is 10, then y=10x + 10. Then when y=90, 10x=80, x=8. Ah! Maybe that's the mistake. If the y - intercept is 10, and the slope is 10 (since from (0,10) to (1,20), 20 - 10=10, so slope 10). Then equation is y=10x + 10. Then when y=90, 10x + 10=90, 10x=80, x=8. So the number of products is 8? But the options have 8 products as an option. Wait, but let's check the graph again. If slope is 10, then (0,10), (1,20), (2,30),..., (8,90). Yes! Because 10*8 + 10=90. So x=8.

Answer:

8 products