Question

what is the slope of the line represented by the equation $f(t)=2t - 6$?

• the slope is 2 and the $y$-intercept is $-6$.
• the slope is $-6$ and the $y$-intercept is 2.
• the slope is 2 and the $y$-intercept is 6.
• the slope is 6 and the $y$-intercept is 2.

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given function $f(t)=2t - 6$, we can think of $y=f(t)$, $x = t$, $m = 2$ and $b=-6$.

Step2: Identify the slope and y - intercept

From the equation $f(t)=2t-6$ (which is in the form $y=mx + b$ with $y = f(t)$ and $x=t$), the coefficient of $t$ (which is equivalent to $x$ in the standard slope - intercept form) is the slope. So the slope $m = 2$. The constant term is the y - intercept, so the y - intercept $b=-6$.

Answer:

The slope is 2 and the y - intercept is - 6.