To determine the slope and the [tex]\( y \)[/tex]-intercept of a linear function given by the equation [tex]\( y = -10x + 1 \)[/tex], follow these steps:
1. Identify the form of the equation: The given equation [tex]\( y = -10x + 1 \)[/tex] is in the slope-intercept form. The standard form for a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
2. Extract the slope [tex]\( m \)[/tex]: In the equation [tex]\( y = -10x + 1 \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\( -10 \)[/tex]. Therefore, the slope [tex]\( m \)[/tex] is [tex]\( -10 \)[/tex].
3. Extract the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex]: The constant term in the equation is [tex]\( 1 \)[/tex]. Therefore, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\( 1 \)[/tex].
Thus, the correct answer is that the slope is [tex]\(-10\)[/tex], and the [tex]\( y \)[/tex]-intercept is [tex]\( 1 \)[/tex].
So, the correct choice is:
- The slope is -10, and the [tex]\( y \)[/tex]-intercept is 1.
