To determine the slope and the [tex]\( y \)[/tex]-intercept of the linear function represented by the equation [tex]\( y = 9x - 2 \)[/tex], we need to recognize the standard form of a linear equation in slope-intercept form, which is:
[tex]\[ y = mx + b \][/tex]
In this form:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept, which is the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0.
Now, let's compare the given equation [tex]\( y = 9x - 2 \)[/tex] to the slope-intercept form [tex]\( y = mx + b \)[/tex]:
1. The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = 9x - 2 \)[/tex] is 9. This means that the slope [tex]\( m \)[/tex] is 9.
2. The constant term in the equation [tex]\( y = 9x - 2 \)[/tex] is -2. This means that the y-intercept [tex]\( b \)[/tex] is -2.
Therefore, the slope and the y-intercept of the linear function are:
- Slope: [tex]\( 9 \)[/tex]
- Y-intercept: [tex]\( -2 \)[/tex]
Now, look at the given choices:
a) The slope is -2, and the y-intercept is 9.
b) The slope is 2, and the y-intercept is 9.
c) The slope is 9, and the y-intercept is -2.
d) The slope is 9, and the y-intercept is 2.
The correct answer matching our calculations is:
c) The slope is 9, and the y-intercept is -2.
