Suppose $f$ is a linear function with $f ( 7 ) = 25.6$ and $$f ( 12 ) = 39.6$$ . Find an equation for $f$ .
A) $f ( x ) = 0.36 x + 25.6$
B) $f ( x ) = 25.6 x + 0.36$
C) $f ( x ) = 2.8 x + 6$
D) $f ( x ) = 6 x + 2.8$

Question

Quizplus · Accepted Answer

To find the equation of a linear function, we use the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ and the point-slope form of a line. Given $f(7) = 25.6$ and $f(12) = 39.6$, we calculate the slope $m = \frac{39.6 - 25.6}{12 - 7} = \frac{14}{5} = 2.8$. Using the point (7, 25.6) and the slope, the equation becomes $f(x) = 2.8x + b$. To find $b$, we substitute $x = 7$ and $f(x) = 25.6$, resulting in $25.6 = 2.8(7) + b$, which simplifies to $b = 6$. Thus, the equation is $f(x) = 2.8x + 6$.

Suppose fff Is a Linear Function With f(7)=25.6f ( 7 ) = 25.6f(7)=25.6

Suppose $f$ Is a Linear Function With $f ( 7 ) = 25.6$