To convert the equation \(20x + 12y = 72\) into slope-intercept form, which is \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y-intercept), follow these steps:
- Isolate \(y\): Start by moving \(20x\) to the other side of the equation.
\[ 12y = 72 - 20x \]
- Rearrange: This can be rearranged to:
\[ 12y = -20x + 72 \]
- Divide by 12: To solve for \(y\), divide every term by 12.
\[ y = \frac{-20}{12}x + \frac{72}{12} \]
- Simplify the fractions:
- \(\frac{-20}{12}\) simplifies to \(\frac{-5}{3}\).
- \(\frac{72}{12}\) simplifies to \(6\).
Putting it all together, the slope-intercept form of the equation is:
\[ y = -\frac{5}{3}x + 6 \]
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