To find the slope and [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = 8 - 7x \)[/tex], we need to recognize that this equation is in the slope-intercept form, which is generally written as:
[tex]\[ y = mx + b \][/tex]
In this form:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept of the line.
Let's compare the given equation [tex]\( y = 8 - 7x \)[/tex] to the slope-intercept form [tex]\( y = mx + b \)[/tex]:
[tex]\[ y = -7x + 8 \][/tex]
From this equation, we can see:
- The term [tex]\( -7x \)[/tex] tells us that the slope [tex]\( m \)[/tex] is [tex]\(-7\)[/tex].
- The constant term [tex]\( 8 \)[/tex] represents the [tex]\( y \)[/tex]-intercept [tex]\( b = 8 \)[/tex].
Therefore:
- The slope of the line is [tex]\(-7\)[/tex].
- The [tex]\( y \)[/tex]-intercept of the line is [tex]\( 8 \)[/tex].
In summary:
- Slope: [tex]\(-7\)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( 8 \)[/tex]
