Equation of a curve passing through (1,2)

[lude1]

Homework Statement

A curve has slope 2x + 3 at each point (x, y) on the curve. Which of the following is an equation for this curve if it pases through the point (1,2)?

Answer: y= x² + 3x - 2

Homework Equations

y= mx + b

The Attempt at a Solution

If the slope is 2x + 3, then that means it is the derivative. Since I a point (1,2), I can find m and b.

m = 2(1) + 3 = 5​

Thus,

2 = 5(1) + b
b = -3​

Therefore, my equation is

y= 5x - 3​

But this isn't correct. What am I doing wrong?

 

[vela]

You found the equation of the tangent to the curve at (1,2), not the equation of the curve.

 

[jtyler05si]

You found the equation of the tangent to the curve at (1,2), not the equation of the curve.

i agree.
To find the equation of the curve you will be doing some integration.