To identify the slope and the [tex]\( y \)[/tex]-intercept of the linear function [tex]\( y = 4x - 9 \)[/tex], we can compare it to the standard form of a linear equation, 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.
1. Identify the Slope ([tex]\( m \)[/tex]):
In the given function [tex]\( y = 4x - 9 \)[/tex], the coefficient of [tex]\( x \)[/tex] is 4. Therefore, the slope [tex]\( m \)[/tex] is:
[tex]\[ m = 4 \][/tex]
2. Identify the [tex]\( y \)[/tex]-Intercept ([tex]\( b \)[/tex]):
In the given function [tex]\( y = 4x - 9 \)[/tex], the constant term is [tex]\(-9\)[/tex]. This term represents the [tex]\( y \)[/tex]-intercept, which is the point where the line crosses the [tex]\( y \)[/tex]-axis. Hence, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is:
[tex]\[ b = -9 \][/tex]
In coordinate form, this intercept is represented as the point [tex]\((0, b)\)[/tex]. Therefore, the [tex]\( y \)[/tex]-intercept is:
[tex]\[ (0, -9) \][/tex]
Summarizing the results:
- The slope of the function [tex]\( y = 4x - 9 \)[/tex] is 4.
- The [tex]\( y \)[/tex]-intercept of the function is [tex]\( (0, -9) \)[/tex].
By comparing these findings with the choices given:
- A. The slope is -9. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 4) \)[/tex].
- B. The slope is 4. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 9) \)[/tex].
- C. The slope is 4. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, -9) \)[/tex].
- D. The slope is 9. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 4) \)[/tex].
The correct choice is:
- C. The slope is 4. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, -9) \)[/tex].
