Suppose $f$ is a linear function with $f ( 6 ) = 20.98$ and $f ( 10 ) = 30.3$ . Find an equation for $f$ .
A) $f ( x ) = 0.43 x + 20.98$
B) $f ( x ) = 20.98 x + 0.43$
C) $f ( x ) = 2.33 x + 7$
D) $f ( x ) = 7 x + 2.33$

Question

Quizplus · Accepted Answer

To find the equation of a linear function $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept, we first calculate the slope $m = \frac{f(10) - f(6)}{10 - 6} = \frac{30.3 - 20.98}{4} = \frac{9.32}{4} = 2.33$. Then, to find $b$, we can use one of the given points, for example, $f(6) = 20.98$, so $20.98 = 2.33 \cdot 6 + b$, solving for $b$ gives $b = 20.98 - 13.98 = 7$. Therefore, the equation is $f(x) = 2.33x + 7$.

Suppose fff Is a Linear Function With f(6)=20.98f ( 6 ) = 20.98f(6)=20.98

Suppose $f$ Is a Linear Function With $f ( 6 ) = 20.98$