The initial value is the ————— in a linear function.

O Slope

O Y
Y-value

OY-intercept

O X-value

Y-intercept

The initial value, or y-intercept, is the output value when the input of a linear function is zero. It is the y-value of the point where the line crosses the y-axis.

Step-by-step explanation:

Initial Value of a Function: Definition and Meaning

A function is a relationship in which there is one input value that equals exactly one output value. A key feature of functions is an initial value. An initial value is exactly what it sounds like: It is a starting value or a starting point.

For instance, say someone is planning on tracking how much they spend on their cell phone bill and apps each month. There is a monthly fee just for the service and some of the apps that they may use can also have subscription fees. The monthly fee for the cell phone service would be the starting cost or initial value.

Another example of initial value would be going to the movie theater to watch a movie. The price of cost of a ticket would be the starting cost or initial value, and any snacks or drinks one might purchase would be extra.

In math, an initial value of a function means that it is the y-intercept of the function. Knowing the y-intercept will help in graph functions. For instance, if the function is f(x)=2x+3f(x)=2x+3, the y intercept, (initial value) is 33. This value is graphed on the y axis. One can then use the slope, 22, to graph a second point and then graph a line through those two points. The following image shows the y-intercept of the function f(x)=2x+3f(x)=2x+3 and a second point found by using the slope, 22.