We are given that the slope of line $b$ is $m = -3$ and it passes through the point $(4, 8)$. To find the y-intercept ($b$) of the line, we can use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Where:

• $m$ is the slope
• $(x_1, y_1)$ is a point on the line

Substituting the given values:

• $m = -3$
• $x_1 = 4$, $y_1 = 8$

We get:

$y - 8 = -3(x - 4)$

Now, simplify the equation to find the y-intercept:

$y - 8 = -3x + 12$

Add 8 to both sides:

$y = -3x + 20$

Thus, the y-intercept is $b = 20$.

Summary:

The y-intercept of the line is $20$.

Would you like further explanation or have any questions? Here are some related questions you might find interesting:

1. How do you derive the equation of a line from two points?
2. What is the significance of the slope-intercept form of a linear equation?
3. How can you find the equation of a line when given only the slope and one point?
4. What does the slope of a line represent geometrically?
5. How can you graph a line from its equation $y = -3x + 20$?

Tip: Always check if the slope is given or if you need to calculate it from two points. The slope-intercept form makes it easy to find the y-intercept once you have the slope and one point!