To write the equation of a line in slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), we first need to derive it from the provided line equation and information about the slope and point.
However, the equation you've given is \( x + y = 3 \). We can manipulate this equation to slope-intercept form first to identify the slope.
Step 1: Convert to slope-intercept form
Starting from: \[ x + y = 3 \]
We can isolate \( y \): \[ y = -x + 3 \]
Here, we can see that the slope \( m \) of the line is \( -1 \).
Step 2: Write the equation of the line with the given slope and point
If you have a specific slope and point (let's denote this point as \( (x_1, y_1) \)), you can then use the point-slope form of the line, which is: \[ y - y_1 = m(x - x_1) \]
Step 3: Rearranging to slope-intercept form
Once you apply the point-slope form, you can then rearrange it into slope-intercept form.
If you provide the point and the slope that you want to use, I can help you write that specific equation in slope-intercept form!