What is the equation of a line with an x-intercept of –6 and a y-intercept of 27?

To find the equation of a line given its x-intercept and y-intercept, we use the intercept form of the line equation:

\[ \frac{x}{a} + \frac{y}{b} = 1 \]

where \(a\) is the x-intercept and \(b\) is the y-intercept.

Given:
- x-intercept (\(a\)) = –6
- y-intercept (\(b\)) = 27

Plugging these values into the equation, we get:

\[ \frac{x}{-6} + \frac{y}{27} = 1 \]

To rewrite this in the slope-intercept form \(y = mx + c\), we need to solve for \(y\):

1. Multiply through by the denominators to clear the fractions:
\[ 27x + (-6)y = -162 \]

2. Simplify and rearrange to the slope-intercept form \(y = mx + c\):
\[ -6y = -27x - 162 \]
\[ y = \frac{27}{6}x + \frac{162}{6} \]
\[ y = 4.5x + 27 \]

So, the equation of the line in slope-intercept form is:
\[ y = 4.5x + 27 \]

Would you like more details or have any questions about this? Here are some additional questions you might want to explore:

1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How do you convert from slope-intercept form to standard form?
4. What are the steps to graph a linear equation using its intercepts?
5. Can you explain how to find the equation of a line parallel or perpendicular to a given line?

**Tip:** Always double-check your intercepts by plugging them back into the final equation to ensure accuracy.

Discover how to find the equation of a line with an x-intercept of -6 and a y-intercept of 27. This detailed solution covers the intercept form and slope-intercept form of the line equation, including step-by-step conversion and simplification. Ideal for students in Grades 7-9.

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