Put the following equation of a line into slope-intercept form, simplifying all fractions. 12x - 20y = 60
Understand the Problem
The question is asking to convert the given linear equation, 12x - 20y = 60, into slope-intercept form (y = mx + b) and to simplify any fractions that may arise in the process.
Answer
$$ y = \frac{3}{5}x - 3 $$
Answer for screen readers
The slope-intercept form of the given equation is: $$ y = \frac{3}{5}x - 3 $$
Steps to Solve
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Start with the original equation We begin with the equation in standard form: $$ 12x - 20y = 60 $$
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Rearrange to isolate $y$ To put the equation in slope-intercept form, we want to isolate $y$. Start by moving the $12x$ term to the right side: $$ -20y = -12x + 60 $$
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Divide by -20 to solve for $y$ Next, divide every term by -20 to get $y$ by itself: $$ y = \frac{-12}{-20}x + \frac{60}{-20} $$
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Simplify the fractions Now simplify the fractions. The first fraction becomes: $$ \frac{-12}{-20} = \frac{3}{5} $$ And the second fraction becomes: $$ \frac{60}{-20} = -3 $$ So we rewrite the equation as: $$ y = \frac{3}{5}x - 3 $$
The slope-intercept form of the given equation is: $$ y = \frac{3}{5}x - 3 $$
More Information
The slope-intercept form ($y = mx + b$) allows us to easily identify the slope ($m$) and the y-intercept ($b$) of the line. In this case, the slope is $\frac{3}{5}$, indicating that for every 5 units moved horizontally, the line rises by 3 units. The y-intercept is -3, meaning the line crosses the y-axis at that point.
Tips
- Forgetting to change the sign when moving terms across the equals sign.
- Not simplifying fractions properly, which can lead to incorrect slope or intercept values.
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