To identify the slope and [tex]\( y \)[/tex]-intercept of the function [tex]\( y = -2x + 3 \)[/tex], we need to recognize the components of the linear equation in its slope-intercept form, which is given by:
[tex]\[ y = mx + b \][/tex]
Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
Given the equation:
[tex]\[ y = -2x + 3 \][/tex]
we can identify the slope ([tex]\( m \)[/tex]) and the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) as follows:
1. Slope ([tex]\( m \)[/tex]): The coefficient of [tex]\( x \)[/tex] in the equation is -2. Hence, the slope is:
[tex]\[ m = -2 \][/tex]
2. [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]): The constant term in the equation is 3. This means the [tex]\( y \)[/tex]-intercept is at:
[tex]\[ b = 3 \][/tex]
The [tex]\( y \)[/tex]-intercept can also be written as the point [tex]\((0, 3)\)[/tex] because it is the point where the line crosses the [tex]\( y \)[/tex]-axis (i.e., where [tex]\( x = 0 \)[/tex]).
Therefore, the correct answer is:
D. The slope is -2. The [tex]\( y \)[/tex]-intercept is (0,3).
