To find the y-intercept of the line given by the equation \( x + 2y = 6 \), we first need to rewrite it in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Let's isolate \( y \):
-
Start with the original equation: \[ x + 2y = 6 \]
-
Subtract \( x \) from both sides: \[ 2y = -x + 6 \]
-
Divide each term by 2: \[ y = -\frac{1}{2}x + 3 \]
From this equation, we can see that the slope \( m \) is \( -\frac{1}{2} \) (which is negative), and the y-intercept \( b \) is \( 3 \).
So, the correct answer is:
- The slope is negative.
- The y-intercept is \( 3 \).
8 answers