Suppose $f$ is a linear function of $x$ . The slope is 2.44. An increase of 6 units in $x$ causes what change in $f$ ?
A) A decrease of 14.64 units
B) An increase of 14.64 units
C) An increase of 2.46 units
D) A decrease of 2.46 units

Question

Quizplus · Accepted Answer

Since $f$ is a linear function of $x$, we can write its equation as:

$f(x) = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

The problem tells us that the slope is 2.44, so we have:

$f(x) = 2.44x + b$

To find out what happens to $f$ when $x$ increases by 6 units, we need to find the value of $f(x + 6)$. We have:

$f(x + 6) = 2.44(x + 6) + b$

We don't know the value of $b$, but we don't need it, because we only need to find the difference between $f(x + 6)$ and $f(x)$. We have:

$$\begin{aligned} f(x + 6) - f(x) &= (2.44(x + 6) + b) - (2.44x + b) \ &= 2.44x + 14.64 - 2.44x \ &= 14.64 \end{aligned}$$

Therefore, an increase of 6 units in $x$ causes an increase of 14.64 units in $f$. The answer is (B).

Suppose fff Is a Linear Function Of xxx the Slope Is 2

Suppose $f$ Is a Linear Function Of $x$ the Slope Is 2