An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem asks to find the equation parallel to y = − 2 x + 13 . Parallel lines have the same slope. The slope of the given line is − 2 . Among the options, y = − 2 x − 5 also has a slope of − 2 . Therefore, the parallel equation is y = − 2 x − 5 .
Explanation
Understanding the Problem We are given the equation of a line: y = − 2 x + 13 . We need to find which of the given equations is parallel to this line.
Parallel Lines and Slopes Two lines are parallel if and only if they have the same slope. The given line has a slope of − 2 . We need to find the line among the options that also has a slope of − 2 .
Checking the Slopes Let's examine the given options:
y = 2 1 x − 9 : This line has a slope of 2 1 , which is not equal to − 2 .
y = 2 x + 7 : This line has a slope of 2 , which is not equal to − 2 .
y = − 2 x − 5 : This line has a slope of − 2 , which is equal to the slope of the given line.
y = − 2 1 x + 13 : This line has a slope of − 2 1 , which is not equal to − 2 .
Identifying the Parallel Line The line y = − 2 x − 5 has the same slope as the given line y = − 2 x + 13 . Therefore, these two lines are parallel.
Final Answer The equation parallel to y = − 2 x + 13 is y = − 2 x − 5 .
Examples
Understanding parallel lines is crucial in various real-world applications. For instance, consider designing a road with multiple lanes. To ensure the lanes don't intersect and maintain a constant distance, they must be parallel. Similarly, in architecture, parallel lines are used to create symmetrical and aesthetically pleasing designs. Knowing how to identify parallel lines helps in these practical scenarios.
