Answer :
To determine the slope of the line given by the equation \( x + 2y = 16 \), we need to convert this equation into the slope-intercept form, \( y = mx + b \), where \( m \) represents the slope.
Here are the steps to convert the equation \( x + 2y = 16 \) into slope-intercept form:
1. Start with the provided standard form equation:
[tex]\[ x + 2y = 16 \][/tex]
2. Isolate the \( y \)-term by subtracting \( x \) from both sides:
[tex]\[ 2y = -x + 16 \][/tex]
3. Solve for \( y \) by dividing each term by 2:
[tex]\[ y = \frac{-x}{2} + \frac{16}{2} \][/tex]
4. Simplify the fraction:
[tex]\[ y = -\frac{1}{2}x + 8 \][/tex]
Now the equation is in slope-intercept form \( y = mx + b \).
From this form, we can see that the coefficient of \( x \) (which is \( m \)) is the slope. Therefore, the slope ( \( m \) ) is:
[tex]\[ -0.5 \][/tex]
So, the slope of the line given by the equation [tex]\( x + 2y = 16 \)[/tex] is [tex]\( -0.5 \)[/tex].
Here are the steps to convert the equation \( x + 2y = 16 \) into slope-intercept form:
1. Start with the provided standard form equation:
[tex]\[ x + 2y = 16 \][/tex]
2. Isolate the \( y \)-term by subtracting \( x \) from both sides:
[tex]\[ 2y = -x + 16 \][/tex]
3. Solve for \( y \) by dividing each term by 2:
[tex]\[ y = \frac{-x}{2} + \frac{16}{2} \][/tex]
4. Simplify the fraction:
[tex]\[ y = -\frac{1}{2}x + 8 \][/tex]
Now the equation is in slope-intercept form \( y = mx + b \).
From this form, we can see that the coefficient of \( x \) (which is \( m \)) is the slope. Therefore, the slope ( \( m \) ) is:
[tex]\[ -0.5 \][/tex]
So, the slope of the line given by the equation [tex]\( x + 2y = 16 \)[/tex] is [tex]\( -0.5 \)[/tex].
