To find the slope and y-intercept of the line represented by the equation [tex]\( f(t) = 2t - 6 \)[/tex], we need to express the equation in the standard form of a linear equation, which is [tex]\( f(t) = mt + b \)[/tex]. Here, [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Given the equation:
[tex]\[ f(t) = 2t - 6 \][/tex]
Let's identify the components:
- Slope ([tex]\( m \)[/tex]): The coefficient of [tex]\( t \)[/tex] in the equation represents the slope. In this case, the coefficient is 2.
- Y-Intercept ([tex]\( b \)[/tex]): The constant term in the equation represents the y-intercept. In this case, the constant term is -6.
So, the slope of the line is 2 and the y-intercept is -6.
To answer the multiple-choice question:
- The slope is 2 and the y-intercept is -6.
- The remaining options are incorrect.
Thus, the correct answer is:
[tex]\[ \text{The slope is 2 and the } y \text{-intercept is -6.} \][/tex]
