write equation of line have y intercept 4 and x intercept -1

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.

Learn how to find the equation of a line given its y-intercept (4) and x-intercept (-1). This problem explores key algebraic concepts such as intercepts, linear equations, and solving for slope. Ideal for students in Grades 8-10.

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