What is the $y$-intercept of the function $f(x)=-\frac{2}{9} x+\frac{1}{3}$?
Answer (1)
To find the y -intercept, we set x = 0 in the function.
Substitute x = 0 into the function: f ( 0 ) = − 9 2 ( 0 ) + 3 1 .
Simplify the expression: f ( 0 ) = 0 + 3 1 = 3 1 .
The y -intercept is 3 1 .
Explanation
Understanding the Problem We are given the function f ( x ) = − 9 2 x + 3 1 and asked to find its y -intercept. The y -intercept is the point where the graph of the function intersects the y -axis. This occurs when x = 0 .
Calculating the y-intercept To find the y -intercept, we substitute x = 0 into the function: f ( 0 ) = − 9 2 ( 0 ) + 3 1 f ( 0 ) = 0 + 3 1 f ( 0 ) = 3 1
Final Answer Therefore, the y -intercept of the function f ( x ) = − 9 2 x + 3 1 is 3 1 .
Examples
Imagine you are tracking the height of a plant over time. The function f ( x ) = − 9 2 x + 3 1 could represent the plant's height, where x is the number of days. The y -intercept, 3 1 , tells you the initial height of the plant when you started tracking it (at day 0). Understanding intercepts helps you interpret the starting point in various real-world scenarios, such as initial investments, starting temperatures, or initial amounts of a substance.
