Y=-x+3

The equation \( y = -x + 3 \) represents a linear function in slope-intercept form, where \( y \) is the dependent variable, \( x \) is the independent variable, the coefficient of \( x \) (which is -1) represents the slope of the line, and the constant term (which is 3) represents the y-intercept of the line. Here are some characteristics of this line: 1. **Slope**: The slope of the line is -1, which means that for every unit increase in \( x \), \( y \) decreases by 1 unit. This indicates that the line descends from left to right. 2. **Y-intercept**: The y-intercept is the point where the line crosses the y-axis. For this equation, when \( x = 0 \): \[ y = -0 + 3 = 3 \] Thus, the y-intercept is (0, 3). 3. **X-intercept**: The x-intercept is found by setting \( y = 0 \) and solving for \( x \): \[ 0 = -x + 3 \\ x = 3 \] Thus, the x-intercept is (3, 0). 4. **Graphing**: To graph the line, you can plot the y-intercept (0, 3) and the x-intercept (3, 0), and then draw a straight line through these points. 5. **Domain and Range**: The domain of this linear function is all real numbers, and the range is also all real numbers. If you have any specific questions about this function or need help with graphing or solving related problems, feel free to ask!