Consider the following equation:
-y = -2
Find the x- and y-intercepts, if possible.
The given equation is \(-y = -2\). To simplify this, we multiply both sides by \(-1\), which yields \(y = 2\). This equation represents a horizontal line in the Cartesian plane where every point on the line has a y-coordinate of 2, regardless of the x-coordinate.
To find the y-intercept, we set \(x = 0\) in our simplified equation \(y = 2\). Since the equation \(y = 2\) states that the y-coordinate is always 2 regardless of the value of \(x\), when \(x = 0\), we have \(y = 2\). Thus, the y-intercept is at the point \((0, 2)\), which is often represented simply by the value of \(y\), which is \(2\).
To find the x-intercept, we set \(y = 0\) in the equation \(y = 2\). This leads to the equation \(0 = 2\), which is a mathematical contradiction. Since no value of \(x\) can satisfy this equation, the line never crosses the x-axis. Therefore, the x-intercept is absent.
In a navigation system, imagine a plane flying at a constant altitude of 2 kilometers above sea level. Its path can be represented by the equation \(y = 2\), where \(y\) is the altitude. The plane never hits the sea level (where altitude \(y=0\)), meaning there is no "x-intercept" in this context. However, it always maintains an altitude of 2 km, representing a y-intercept of 2. This helps in understanding that not every function intersects both axes.