Question

a curve passes through the point (4,2) and has the property that the slope of the curve at every point p is three times the y-coordinate p. what is the equation of the curve?:

Answer 1

The slope of the curve at a point (x,y) is given as 3y. This means that the equation of the curve is in the form of y = mx + b, where m is the slope of the curve and b is the y-intercept.

Since the curve passes through the point (4,2), we can use this point to find the value of b:

y = mx + b

2 = 3(4) + b

b = -10

So the curve's equation is: y = 3x - 10

You can confirm this by plugging in the point (4,2) into the equation.

2 = 3(4) - 10

2 = 12 - 10

2 = 2