To determine the slope and the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = -3x - 2 \)[/tex], we need to identify the coefficients in the standard form of the equation for a straight line.
The equation of a line in slope-intercept form is [tex]\( y = mx + c \)[/tex], where: - [tex]\( m \)[/tex] is the slope of the line, and - [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept of the line.
Given the equation [tex]\( y = -3x - 2 \)[/tex]:
1. Identify the slope: The coefficient of [tex]\( x \)[/tex] in the equation is [tex]\(-3\)[/tex]. Hence, the slope [tex]\( m \)[/tex] is [tex]\(-3\)[/tex].
2. Identify the [tex]\( y \)[/tex]-intercept: The constant term in the equation is [tex]\(-2\)[/tex]. Hence, the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is [tex]\(-2\)[/tex].
Now, let's match these results with the options provided:
A. Slope [tex]\( = -3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = 2 \)[/tex]
B. Slope [tex]\( = 3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = -2 \)[/tex]
C. Slope [tex]\( = 3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = 2 \)[/tex]
D. Slope [tex]\( = -3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = -2 \)[/tex]
The correct answer is: D. Slope [tex]\( = -3 \)[/tex] and [tex]\( y \)[/tex]-intercept [tex]\( = -2 \)[/tex]
