Questions: Which of the lines in the following graph appear to be tangent lines? Select all that apply. A. L5 B. L6 C. L4 E. L1 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 selected tangent line appears to be undefined. The other line(s) are parallel to the graph at the point of tangency. - B. 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. - C. 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. - D. The slope of each tangent line is approximately zero. The slope(s) of the other line(s) are undefined.

Which of the lines in the following graph appear to be tangent lines? Select all that apply.
A. L5
B. L6
C. L4
E. L1
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 selected tangent line appears to be undefined. The other line(s) are parallel to the graph at the point of tangency.
- B. 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.
- C. 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.
- D. The slope of each tangent line is approximately zero. The slope(s) of the other line(s) are undefined.

Transcript text: Which of the lines in the following graph appear to be tangent lines? Select all that apply. $\square$ A. $L_{5}$ $\square$ B. $L_{6}$ $\square$ C. $L_{4}$ $\square$ E. $\mathrm{L}_{1}$ 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 selected tangent line appears to be undefined. The other line(s) are parallel to the graph at the point of tangency. - B. 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. - C. 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. - D. The slope of each tangent line is approximately zero. The slope(s) of the other line(s) are undefined.

Solution

Solution Steps

Step 1: Identifying Tangent Lines

Tangent lines touch the curve at a single point and have the same slope as the curve at that point. Lines L₁, L₃, and L₆ appear to be tangent.

Step 2: Eliminating Non-Tangent Lines

L₂, L_4, and L₅ are not tangent lines. L₂ and L₄ clearly intersect the curve at more than one point. L₅ appears to touch at one point, but it doesn't have the same slope as the curve at that point; it looks more like a horizontal line while the curve's slope at that point is not zero.

Step 3: Explaining Tangency and Non-Tangency

The selected lines (L₁, L₃, and L₆) appear tangent because they seem to touch the curve at a single point and have the same slope as the curve at that point. The other lines either intersect the curve at multiple points or do not have the same slope as the curve at the point of intersection.

Final Answer

The lines that appear to be tangent are L₁, L₃, and L₆. The correct explanation is C. 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.

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