An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the slope using two points from the table: m = 5 − 0 − 10 − ( − 20 ) = 2 .
Identify the y-intercept from the table: y = − 20 when x = 0 .
The slope is 2 and the y-intercept is -20.
The final answer is slope: 2 , y -intercept: − 20 .
Explanation
Understanding the Problem We are given a table of values representing the total savings, y , based on the number of coupons, x , used from a coffee shop coupon book. Our goal is to find the slope and y -intercept of the line represented by these points.
Calculating the Slope The slope of a line can be calculated using any two points on the line. Let's use the points (0, -20) and (5, -10) from the table. The slope, m , is given by the formula: m = x 2 − x 1 y 2 − y 1 Substituting the coordinates of the points, we get: m = 5 − 0 − 10 − ( − 20 ) = 5 − 10 + 20 = 5 10 = 2 So, the slope of the line is 2.
Identifying the y-intercept The y -intercept is the value of y when x = 0 . From the table, we can see that when x = 0 , y = − 20 . Therefore, the y -intercept is -20.
Final Answer Therefore, the slope of the line is 2 and the y -intercept is -20.
Examples
Understanding the slope and y-intercept of a line is useful in many real-world scenarios. For example, if you are tracking the cost of a taxi ride, the y-intercept might represent the initial fee, and the slope would represent the cost per mile. Similarly, in business, the y-intercept could represent the fixed costs of production, and the slope could represent the variable cost per unit produced. By understanding these concepts, you can make informed decisions and predictions in various situations.
The electric device delivers a current of 15.0A for 30 seconds, resulting in a total charge of 450C. This equals approximately 2.81 x 10^21 electrons flowing through the device. Therefore, about 2.81 x 10^21 electrons flow in 30 seconds.
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