CPM Homework Help : APCALC Problem 7-209

Multiple Choice: A point is moving along a curve $y = f(x)$ . At the instant when the slope of the curve is $-\frac { 1 } { 3 }$ , the $x$ -coordinate of the moving point is increasing at a rate of $5$ units per second. The rate of change, in units per second, of the $y$ -coordinate of the point is:

$-\frac { 5 } { 3 }$

$-\frac { 1 } { 3 }$

$\frac { 1 } { 3 }$

$\frac { 5 } { 3 }$

$\frac { 3 } { 5 }$

Hint:

$\text{Slope}=\frac{\text{rise}}{\text{run}},\text { where run is the change in the }x\text{-coordinate and rise is the change in the }y\text{-coordinate.}$

Solve for rise.

Steps:

$\text{slope}=-\frac{1}{3}=\frac{\Delta y}{\Delta x}$

$-\Delta x=3\Delta y$

Implicitly differentiate with respect to $t$ .