slope-inte rcept form 1. \( x+y=1 \rightarrow \)

To convert the equation \( x + y = 1 \) into **slope-intercept form**, which is \( y = mx + b \), follow these steps: 1. **Start with the original equation:** \[ x + y = 1 \] 2. **Isolate \( y \) by subtracting \( x \) from both sides:** \[ y = -x + 1 \] 3. **Now, the equation is in slope-intercept form:** \[ y = -x + 1 \] - **Slope (\( m \))**: The coefficient of \( x \) is **-1**. This means the line slopes downward. - **Y-intercept (\( b \))**: The constant term is **1**. This is the point where the line crosses the y-axis at \( (0, 1) \). **Graphical Interpretation:** - **Slope (\( m = -1 \))**: For every 1 unit increase in \( x \), \( y \) decreases by 1 unit. - **Y-intercept (\( b = 1 \))**: The line crosses the y-axis at the point \( (0, 1) \). **Summary:** \[ x + y = 1 \quad \text{is equivalent to} \quad y = -x + 1 \] where: - **Slope (\( m \))** = -1 - **Y-intercept (\( b \))** = 1