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locachola17
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Homework Statement
A curve passes through the point (0, 9) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
locachola17 said:Homework Statement
A curve passes through the point (0, 9) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?
Homework Equations
The Attempt at a Solution
locachola17 said:okay well at the point (0,9) the y-coordinate is 9
if the slope is twice the y-coordinate, the slope is 18?!
locachola17 said:dy/dx is 2y
lanedance said:but the question says its true for every point on the line...
locachola17 said:y(x)=y^2
locachola17 said:you integrate both sides?
The equation of a curve passing through (0, 9) is y = 9. This is because when x = 0, the value of y will always be 9.
To find the equation of a curve passing through (0, 9), you need to have at least one other point on the curve. Once you have another point, you can use the slope-intercept form of a line (y = mx + b) and substitute the coordinates of the point to solve for the slope (m) and the y-intercept (b). Then, you can write the equation as y = mx + b with the values you found.
Yes, there can be multiple equations for a curve passing through (0, 9). This is because there are infinite curves that can pass through a single point. However, if you have additional information or constraints, such as the type of curve or another point it passes through, you can narrow down the possible equations.
The point (0, 9) represents the y-intercept of the curve. This means that when x = 0, the value of y will always be 9. This point is important in determining the equation of the curve as it helps to find the y-intercept.
Yes, the equation of a curve passing through (0, 9) can be a straight line. This is because a straight line can pass through any point, including (0, 9). If the curve is a straight line, the equation will be in the form y = mx + b, where m is the slope and b is the y-intercept.