Put the following equation of a line into slope-intercept form, simplifying all fractions: 3x + 15y = -60.
Understand the Problem
The question is asking to convert the given equation of a line, represented as 3x + 15y = -60, into slope-intercept form (y = mx + b) while simplifying any fractions.
Answer
The slope-intercept form of the equation is: $$ y = -\frac{1}{5}x - 4 $$
Answer for screen readers
The slope-intercept form of the equation is:
$$ y = -\frac{1}{5}x - 4 $$
Steps to Solve
- Isolate the $y$ term
Start with the equation:
$$ 3x + 15y = -60 $$
To isolate the $y$ term, subtract $3x$ from both sides:
$$ 15y = -3x - 60 $$
- Divide by the coefficient of $y$
Now, divide every term by $15$ to solve for $y$:
$$ y = \frac{-3x}{15} - \frac{60}{15} $$
This simplifies to:
$$ y = -\frac{1}{5}x - 4 $$
- Present in slope-intercept form
The final equation in slope-intercept form is:
$$ y = -\frac{1}{5}x - 4 $$
The slope-intercept form of the equation is:
$$ y = -\frac{1}{5}x - 4 $$
More Information
In slope-intercept form, the equation provides useful insight: the slope of the line is $-\frac{1}{5}$, indicating that for every 5 units moved horizontally, the line decreases by 1 unit vertically. The y-intercept is -4, which is where the line crosses the y-axis.
Tips
- Forgetting to subtract the $3x$ term from both sides, which can lead to an incorrect expression for $y$.
- Not simplifying fractions completely. Always ensure that fractions are reduced to their simplest form.
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