Sure! To write the equation [tex]\( y + x = 3 \)[/tex] in slope-intercept form, we will follow these steps:
1. Identify the Original Equation:
The given equation is:
[tex]\[
y + x = 3
\][/tex]
2. Isolate [tex]\( y \)[/tex]:
We need to rearrange the given equation to solve for [tex]\( y \)[/tex]. Subtract [tex]\( x \)[/tex] from both sides of the equation to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 3 - x
\][/tex]
3. Re-write in Slope-Intercept Form:
The slope-intercept form of a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept. Compare [tex]\( y = 3 - x \)[/tex] with [tex]\( y = mx + b \)[/tex]:
[tex]\[
y = -x + 3
\][/tex]
4. Identify the Slope and Y-Intercept:
From the equation [tex]\( y = -x + 3 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( 3 \)[/tex].
So, the equation [tex]\( y + x = 3 \)[/tex] written in slope-intercept form is [tex]\( y = -x + 3 \)[/tex], where the slope [tex]\( m \)[/tex] is [tex]\(-1\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\( 3 \)[/tex].
