Question

what is the y - intercept in a linear function?
the slope of the line in the equation f(x) = mx + b.
the point where the line crosses the y - axis, represented by the value of b in the equation f(x) = mx + b.
the value of x when y equals zero.
the point where the line crosses the x - axis.

Explanation:

To determine the y - intercept of a linear function \( f(x)=mx + b \), we recall the definition of the y - intercept. The y - intercept is the point where the graph of the line crosses the y - axis. On the y - axis, the value of \( x = 0 \). If we substitute \( x = 0 \) into the linear equation \( f(x)=mx + b \), we get \( f(0)=m\times0 + b=b \). So the y - intercept is represented by the value of \( b \) in the equation \( f(x)=mx + b \), which is the point where the line crosses the y - axis.

Answer:

The point where the line crosses the y - axis, represented by the value of \( b \) in the equation \( f(x)=mx + b \).