An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Substitute each coordinate into the equation y = 2 x − 4 .
Check if the equation holds true for each coordinate.
Coordinate A: ( − 1 , 2 ) gives 2 = 2 ( − 1 ) − 4 , which is false.
Coordinate B: ( 2 , − 4 ) gives − 4 = 2 ( 2 ) − 4 , which is false.
Coordinate C: ( 1 , − 2 ) gives − 2 = 2 ( 1 ) − 4 , which is true.
Coordinate D: ( − 3 , − 5 ) gives − 5 = 2 ( − 3 ) − 4 , which is false.
The coordinate that satisfies the equation is ( 1 , − 2 ) ​ .

Explanation

Understanding the Problem We are given the equation of a line y = 2 x − 4 and four coordinate points. Our goal is to determine which of these points lies on the line. A point lies on the line if its coordinates satisfy the equation of the line. We will substitute the x and y values of each coordinate into the equation and check if the equation holds true.

Checking Coordinate A Let's check coordinate A: ( − 1 , 2 ) . Substitute x = − 1 and y = 2 into the equation y = 2 x − 4 . We get 2 = 2 ( − 1 ) − 4 , which simplifies to 2 = − 2 − 4 , or 2 = − 6 . This is false, so point A is not on the line.

Checking Coordinate B Now, let's check coordinate B: ( 2 , − 4 ) . Substitute x = 2 and y = − 4 into the equation y = 2 x − 4 . We get − 4 = 2 ( 2 ) − 4 , which simplifies to − 4 = 4 − 4 , or − 4 = 0 . This is false, so point B is not on the line.

Checking Coordinate C Next, let's check coordinate C: ( 1 , − 2 ) . Substitute x = 1 and y = − 2 into the equation y = 2 x − 4 . We get − 2 = 2 ( 1 ) − 4 , which simplifies to − 2 = 2 − 4 , or − 2 = − 2 . This is true, so point C lies on the line.

Checking Coordinate D Finally, let's check coordinate D: ( − 3 , − 5 ) . Substitute x = − 3 and y = − 5 into the equation y = 2 x − 4 . We get − 5 = 2 ( − 3 ) − 4 , which simplifies to − 5 = − 6 − 4 , or − 5 = − 10 . This is false, so point D is not on the line.

Conclusion Therefore, the only coordinate that lies on the line y = 2 x − 4 is C: ( 1 , − 2 ) .


Examples
Understanding linear equations is crucial in many real-world applications. For instance, in economics, a linear equation can represent a supply curve, where the quantity of a product supplied is related to its price. If the equation is y = 2 x − 4 , where y is the quantity supplied and x is the price, we can determine the supply at a specific price point. Knowing which coordinates satisfy this equation helps economists predict market behavior and make informed decisions about production and pricing strategies. Similarly, in physics, linear equations can describe motion, and in engineering, they can model the behavior of circuits or structures.

Answered by GinnyAnswer | 2025-07-08

To find how many electrons flow through a device delivering a current of 15.0 A for 30 seconds, we first calculate the total charge as 450 C, then divide this charge by the charge of one electron (about 1.6 x 10^-19 C). This results in approximately 2.81 x 10^21 electrons flowing through the device.
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Answered by Anonymous | 2025-08-04