Find the y-intercept of the line represented by the equation below.
$-2x + 5 = y$
The problem asks for the y-intercept of the line given by the equation \(-2x + 5 = y\). The y-intercept of any line is the point where the line intersects the y-axis. At this point, the x-coordinate is always zero. Thus, finding the y-intercept involves calculating the value of y when \(x = 0\).
To find the y-intercept, we substitute \(x = 0\) into the given equation:
\[-2(0) + 5 = y\]
Performing the multiplication, we have:
\[0 + 5 = y\]
Which simplifies to:
\[y = 5\]
Therefore, the line intersects the y-axis at the point where \(y = 5\). This point is typically represented as \((0, 5)\). The y-intercept is the value \(y=5\).
In conclusion, by setting \(x=0\) in the linear equation \(-2x + 5 = y\), we determine that the y-intercept is \(\boxed{5}\).
The concept of a y-intercept is vital in real-world scenarios such as business or physics. For example, if you are tracking the amount of battery life remaining on your phone over time, the equation could be \(L(t) = -5t + 100\), where \(L\) is the percentage and \(t\) is the hours of usage. The y-intercept, which is \(100\), represents the initial battery charge of \(100\%\) when the usage time is \(0\) hours. Understanding the intercept helps you determine starting values for various linear relationships.