Write an equation for the linear function f satisfying the given conditions.
-$f ( 3 ) = 5$ and $f ( 6 ) = 6$
A) $f ( x ) = \frac { 1 } { 3 } x + 4$
B) $f ( x ) = \frac { 7 } { 3 } x - 2$
C) $f ( x ) = \frac { 2 } { 3 } x + 3$
D) $f ( x ) = \frac { 4 } { 3 } x - 2$

Question

Quizplus · Accepted Answer

The slope $m$ of the line can be calculated using the two given points $(3,5)$ and $(6,6)$ as $m = \frac{6-5}{6-3} = \frac{1}{3}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say $(3,5)$, we get $y - 5 = \frac{1}{3}(x - 3)$. Simplifying this equation to the slope-intercept form $y = mx + b$ gives $y = \frac{1}{3}x + 4$, which matches choice A.

Write an Equation for the Linear Function F Satisfying the Given