To determine the slope and [tex]\( y \)[/tex]-intercept of the given equation [tex]\( 7x + y = 8 \)[/tex], we will convert it to the slope-intercept form, which is [tex]\( y = mx + b \)[/tex]. In this form, [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
Starting with the original equation:
[tex]\[ 7x + y = 8 \][/tex]
We need to solve for [tex]\( y \)[/tex]. To isolate [tex]\( y \)[/tex], we can subtract [tex]\( 7x \)[/tex] from both sides of the equation:
[tex]\[ y = -7x + 8 \][/tex]
Now, the equation is in the slope-intercept form [tex]\( y = mx + b \)[/tex]. From this expression, we can see that:
- The slope ([tex]\( m \)[/tex]) is [tex]\(-7\)[/tex]
- The [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is [tex]\( 8 \)[/tex]
So, the slope of the graph is [tex]\(-7\)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( 8 \)[/tex].
Thus, the correct answer is:
D) Slope [tex]\( = -7 \)[/tex], [tex]\( y \)[/tex]-intercept [tex]\( = 8 \)[/tex]
