Question

A point moves along the curve 4y−4y+9x=2. When the point is at (−10/9), -1), its x-coordinate is increasing at the rate of 5 units per second. How fast is its y-coordinate changing at that instant of time?

a. -7/4 units/sec
b. 15/4 units/sec
c. -15/4 units/sec
d. 23/4 units/sec

Answer 1

Please check the equation.

Explanation:

As written, the equation 4y−4y+9x=2 reduces to 9x = 2, or x = (2/9). This is a vertical line in which all values of y are possible when x = 2.

Point ((-10/9),-1) can't fall on this line.

If the correct equation is linear, the the slope of the line will be the rate of change for all points on the line. If the line is non-linear, take the first derivative of the equation and solve for x = (-10/9). That will be the rate of change at that point.