To identify the slope and the [tex]\( y \)[/tex]-intercept of the function [tex]\( y = 4x - 9 \)[/tex], let's break down the elements of the equation in the slope-intercept form.
The slope-intercept form of a linear equation is given by:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope,
- [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
Let's compare the given equation [tex]\( y = 4x - 9 \)[/tex] with the general form [tex]\( y = mx + b \)[/tex]:
1. Determining the Slope:
The slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex]. In this equation, the coefficient of [tex]\( x \)[/tex] is 4. Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[ m = 4 \][/tex]
2. Determining the [tex]\( y \)[/tex]-Intercept:
The [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is the constant term in the equation. In [tex]\( y = 4x - 9 \)[/tex], the constant term is -9. Therefore, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is:
[tex]\[ b = -9 \][/tex]
The [tex]\( y \)[/tex]-intercept is represented as the point where the line crosses the [tex]\( y \)[/tex]-axis. This occurs when [tex]\( x = 0 \)[/tex]. Hence, the [tex]\( y \)[/tex]-intercept in coordinate form is:
[tex]\[ (0, -9) \][/tex]
Now, let's match these values with the options provided:
A. The slope is -9. The [tex]\( y \)[/tex]-intercept is (0, 4).
B. The slope is 4. The [tex]\( y \)[/tex]-intercept is (0, -9).
C. The slope is 9. The [tex]\( y \)[/tex]-intercept is (0, 4).
D. The slope is 4. The [tex]\( y \)[/tex]-intercept is (0, 9).
Comparing our results:
- The slope is 4.
- The [tex]\( y \)[/tex]-intercept is [tex]\( (0, -9) \)[/tex].
Thus, the correct option is:
[tex]\[ \boxed{B} \text{ The slope is 4. The \( y \)-intercept is (0, -9).} \][/tex]
