To determine the slope of the linear equation [tex]\( y + 2x = 5 \)[/tex], we need to rewrite it in the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Here are the steps to find the slope:
1. Start with the given equation:
[tex]\[
y + 2x = 5
\][/tex]
2. Isolate [tex]\( y \)[/tex] on one side of the equation. To do this, we need to subtract [tex]\( 2x \)[/tex] from both sides:
[tex]\[
y = -2x + 5
\][/tex]
3. Now the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex] and [tex]\( b \)[/tex] is the constant term.
4. Identify the slope [tex]\( m \)[/tex] from the equation [tex]\( y = -2x + 5 \)[/tex]:
[tex]\[
m = -2
\][/tex]
Therefore, the slope of the equation [tex]\( y + 2x = 5 \)[/tex] is [tex]\(\boxed{-2}\)[/tex].
