### Home > CALC3RD > Chapter Ch7 > Lesson 7.4.3 > Problem7-209

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:

 $-\frac { 5 } { 3 }$ $-\frac { 1 } { 3 }$ $\frac { 1 } { 3 }$ $\frac { 5 } { 3 }$ $\frac { 3 } { 5 }$

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

Solve for rise.

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

$-\Delta x=3\Delta y$

Implicitly differentiate with respect to $t$.