Which equation represents a line which is parallel to the $y$-axis?
A. $x=-4y$
B. $y=x-3$
C. $x=-8$
D. $y=-7
Answer (1)
Recognize that a line parallel to the y-axis is a vertical line.
Recall that the equation of a vertical line is in the form x = c , where c is a constant.
Identify the equation x = − 8 as matching the form of a vertical line.
Conclude that the equation representing a line parallel to the y -axis is x = − 8 .
Explanation
Understanding the Problem We are given four equations: x = − 4 y , y = x − 3 , x = − 8 , and y = − 7 . We need to identify the equation that represents a line parallel to the y-axis. A line parallel to the y-axis is a vertical line. The equation of a vertical line is of the form x = c , where c is a constant.
Plan of Action Recall that a line parallel to the y-axis is a vertical line, and its equation is of the form x = constant. Examine the given equations and identify the one that matches the form x = constant.
Identifying the Correct Equation The equation x = − 8 is of the form x = constant, where the constant is -8. Therefore, the equation x = − 8 represents a line parallel to the y-axis.
Final Answer The equation that represents a line parallel to the y -axis is x = − 8 .
Examples
Understanding lines parallel to the y-axis is crucial in various real-world applications. For instance, consider a scenario where you're designing a building. If a wall needs to be perfectly vertical, it must be parallel to the y-axis in your architectural plans. Similarly, in robotics, ensuring a robot's arm moves precisely along a vertical plane requires the arm's movement to be parallel to the y-axis. This concept is also fundamental in computer graphics for rendering vertical objects accurately.
