Question

Give precise mathematical definitions or descriptions of each

of the concepts that follow. Then illustrate the definition with

a graph or algebraic example, if possible:

the graphical interpretations of a tangent line and a secant

line to a graph

Short answer

Tangent line: touches a curve at a single point whereas a secant line intersects two or more points on the curve.

Step-by-step solution

Step 1. Given information

Tangent line and secant line.

Tangent line gives a slope of the equation and secant line gives solution here

Step 2. Calculation

Tangent line: touches curve at a point, making the curves slope there.

A secant line intersects two or more points on the curve.

They are the line which extends up-to infinity.

Red curve shows a parabola $y=x^2$where two line intersect curve at different points.

The blue line curve which is tangent line: here the line cut or intersect the curve at only one point of curve.

The green line indicates secant line: here the line intersects the curve at two point so its secant line.

Hence, tangent line: touches a curve at a single point whereas a secant line intersects two or more points on the curve.