Suppose $f$ is a linear function with $f ( 8 ) = 27.92$ and $f ( 11 ) = 35.39$ . Find an equation for $f$ .
A) $f ( x ) = 0.4 x + 27.92$
B) $f ( x ) = 27.92 x + 0.4$
C) $f ( x ) = 2.49 x + 8$
D) $f ( x ) = 8 x + 2.49$

Question

Quizplus · Accepted Answer

Since $f$ is a linear function, we can use the slope-intercept form of a linear equation, which is $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. From the given information, we can find the slope as $\frac{35.39-27.92}{11-8} = 2.49$ and the y-intercept as $\left(0, f(0)\right)$ where $f$ is the linear function. Since $f$ is linear, we know that the y-intercept will be the same as $f(0)$ and so we need to find the value of $f(0)$. To do this, we can use the point-slope form of a linear equation which is $(y-y_1) = m(x-x_1)$ where $(x_1,y_1)$ is a point on the line and $m$ is the slope. We can use $(8,27.92)$ as our point and $m = 2.49$ and then solve for $y$ to get $f(x) = 2.49x + 8$.

Suppose fff Is a Linear Function With f(8)=27.92f ( 8 ) = 27.92f(8)=27.92

Suppose $f$ Is a Linear Function With $f ( 8 ) = 27.92$