A tangent to a curve at a point is a straight line which touches but does not intersect the curve at that point. A slope of the curve at a point is defined as the slope of the tangent at that point on the curve.
Example
Consider the curve y = x^{2 }- 3x + 3. The tangent to the curve at the point (2, 1) is shown below.
Figure
Later, after studying differential calculus, we may show that y = 2x - 3 is the tangent at (2, 1). Therefore, the slope of the curve at (2, 1) is 2.