Question

which of the lines in the following graph appear to be tangent lines? why or why not? which of the lines in the following graph appear to be tangent lines? select all that apply a. l3 b. l6 c. l1 d. l4 e. l5 f. l2 why do the lines selected above appear to be tangent lines, and why are the other line(s) not tangent lines? a. the slope of each tangent line is equal to the slope of the graph at the point of intersection between the graph and the respective tangent line. the other line(s) are not parallel to the graph at the point of tangency b. the slope of each selected tangent line appears to be undefined. the other line(s) are parallel to the graph at the point of tangency c. the slope of each tangent line is approximately zero. the slope(s) of the other line(s) are undefined d. each tangent line is perpendicular to the graph at the point of intersection between the graph and the respective tangent line. the other line(s) are not perpendicular to the graph at the point of tangency

Explanation:

Step1: Recall tangent - line definition

A tangent line touches a curve at one point and has the same slope as the curve at that point.

Step2: Analyze each line

$L_2$, $L_3$, $L_4$, $L_6$ touch the curve at one - point and match the curve's slope at that point. $L_1$ and $L_5$ do not.

Step3: Select correct reason

The slope of each tangent line is equal to the slope of the graph at the point of intersection.

Answer:

A. $L_2$
B. $L_3$
C. $L_4$
D. $L_6$
E. A