# How do you know if a line is tangent to a curve?

##### 1 Answer

Please check the explanation.

#### Explanation:

**By solving the two equations you will get a point #(x,y) # which lies on both the curve and the straight line.
if you got more than one point then this line will be intersecting and not a tangent to the curve.
then by finding the first derivative of the curve and substituting with the value of the point#(x,y)#
if it's value is equal to the slope of the straight line then this line is its tangent. **

**For example** :

determine whether the line

**1)** Finding the **intersection point** :

by solving the two equation the intersection point will be

**2)** Finding the **first derivative** of the curve function:

By substituing with the value of

Which is equal to the slope of the straight line