### Home > CALC > Chapter 7 > Lesson 7.3.5 > Problem7-164

7-164.

Multiple Choice: A point ($x$, $y$) 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 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:

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

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

1. $\frac { 1 } { 3 }$

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

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

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

$\text{slope}=-\frac{1}{3}=\frac{\Delta y}{\Delta x}$
$-\Delta x=3\Delta y$
Implicitly differentiate with respect to $t$.