To put the equation \( 12x - 20y = -40 \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we will solve for \( y \).
Starting with the original equation:
\[ 12x - 20y = -40 \]
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Isolate the term involving \( y \):
Subtract \( 12x \) from both sides:
\[ -20y = -12x - 40 \]
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Divide each term by -20 to solve for \( y \):
\[ y = \frac{-12x}{-20} + \frac{-40}{-20} \]
Simplifying each of these fractions gives:
\[ y = \frac{12}{20} x + 2 \]
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Simplify the fraction \( \frac{12}{20} \):
The greatest common divisor of 12 and 20 is 4, so:
\[ \frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]
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Write the final slope-intercept form:
Thus, the equation in slope-intercept form is:
\[ y = \frac{3}{5}x + 2 \]
So, the equation \( 12x - 20y = -40 \) in slope-intercept form is:
\[ y = \frac{3}{5}x + 2 \]
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