To write the equation \( 0.4x + 0.2y = 0.6 \) in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we need to solve for \( y \).
Starting with the original equation:
\[ 0.4x + 0.2y = 0.6 \]
First, we want to isolate \( y \). We can do this by subtracting \( 0.4x \) from both sides:
\[ 0.2y = 0.6 - 0.4x \]
Next, to solve for \( y \), divide every term by \( 0.2 \):
\[ y = \frac{0.6}{0.2} - \frac{0.4x}{0.2} \]
Calculating \( \frac{0.6}{0.2} \) gives us \( 3 \), and \( \frac{0.4}{0.2} \) gives us \( 2 \):
\[ y = 3 - 2x \]
Rearranging this gives us the slope-intercept form:
\[ y = -2x + 3 \]
So, the equation in slope-intercept form is:
\[ y = -2x + 3 \]