The problem states that $k<0$ and $b>0$. We are asked to determine which quadrant the line $y = kx + b$ does not pass through.

1. Problem Description

The problem states that $k<0$ and $b>0$. We are asked to determine which quadrant the line $y = kx + b$ does not pass through.

2. Solution Steps

The given equation is $y = kx + b$.

Since $k<0$, the slope of the line is negative.

Since $b>0$, the y-intercept of the line is positive.

A line with a negative slope and a positive y-intercept will have the following characteristics:

- It will intersect the y-axis at a positive value (quadrants 1 and 2).

- It will go downwards as x increases.

- Since the slope is negative and the y-intercept is positive, the line must pass through the first and second quadrants. The line must also pass through the fourth quadrant.

- The line cannot pass through the third quadrant.

To confirm, let's examine a few points:

- When $x=0$, $y=b>0$. Thus the line passes through the first or second quadrant.

- As $x$ becomes increasingly positive, $kx$ becomes increasingly negative. Eventually, $kx+b$ will become negative, indicating the line passes through the fourth quadrant.

- When $y=0$, $kx = -b$, so $x = -b/k$. Since $b>0$ and $k<0$, then $-b/k > 0$. Thus the line passes through the first or fourth quadrant.

Therefore, the line does not pass through the third quadrant.

3. Final Answer

C. 第三象限