The equation of a line with a given $y$-intercept $b$ and $x$-intercept $a$ can be written as:

$\frac{x}{a} + \frac{y}{b} = 1$

Given that:

• The $y$-intercept $b = 4$
• The $x$-intercept $a = -1$

Substitute these values into the equation:

$\frac{x}{-1} + \frac{y}{4} = 1$

Simplifying this equation:

$-\frac{x}{1} + \frac{y}{4} = 1$

Multiply through by 4 to eliminate the fraction:

$-4x + y = 4$

Thus, the equation of the line is:

$y = 4x + 4$

Would you like more details or have any questions about this solution?

Here are five related questions to explore further:

1. How do you find the slope of a line from its intercepts?
2. What is the general form of a linear equation?
3. How do you graph a line with known intercepts?
4. How do parallel and perpendicular lines relate in terms of their slopes?
5. How do you convert from standard form to slope-intercept form?

Tip: The slope of a line can be quickly determined if you know the x- and y-intercepts.