Draw the secants of a curve (line?)

In summary: Or maybe it's to demonstrate how secant lines can be used to approximate the slope of a curve. Either way, the equations of the secants can be determined by using the slope formula (m = (y2-y1)/(x2-x1)) and plugging in the given points. In summary, the task is to draw secant lines from the point (2, 60) to various points on the graph and determine their equations using the slope formula.
  • #1
zeion
466
1

Homework Statement


An automobile's distance is given by d = 30t (t in seconds, d in metres):

"Draw the secants from the point (2, 60) to each of the points on the graph ending at t = 3, 2.5, 2.1, 1.01"

"Determine the equations of each of the secants above."

Homework Equations


The Attempt at a Solution



To my understanding, d = 30t is a line.
According to the text, "A line that intersects a curve in two places is called a secant".
How can a line have any secants?
 
Last edited:
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  • #2
A curve in its most liberal interpretation can also include a straight line.
 
  • #3
zeion said:
"Draw the secants from the point (2, 60) to each of the points on the graph ending at t = 3, 2.5, 2.1, 1.01"

How can a point end? :confused:
 
  • #4
Uh I'm not sure, but I'm guessing it's asking me to draw the secant from (2, 60) to these points (3, d(3)), (2.5, d(2.5)), etc.

Though I still don't see the point since they're all going to overlap anyway lol.
 
  • #5
zeion said:
Uh I'm not sure, but I'm guessing it's asking me to draw the secant from (2, 60) to these points (3, d(3)), (2.5, d(2.5)), etc.

Though I still don't see the point since they're all going to overlap anyway lol.

Perhaps the point is to show that for a straight line, all secant lines have the same slope.
 

1. What is a secant?

A secant is a straight line that intersects a curve at two points.

2. How do you draw secants of a curve?

To draw secants of a curve, you need to first identify the points of intersection between the curve and the secant line. Then, use a straight edge or ruler to draw a line connecting these two points.

3. What is the purpose of drawing secants of a curve?

The purpose of drawing secants of a curve is to better understand the behavior of the curve and its relationship to the secant line. It can also help in determining the slope of the curve at a specific point.

4. Can there be more than two secants for a single curve?

Yes, there can be multiple secant lines for a single curve. These secants can have different slopes and can intersect the curve at different points.

5. What is the difference between a secant and a tangent?

A secant is a straight line that intersects a curve at two points, while a tangent is a straight line that intersects a curve at only one point, known as the point of tangency. In other words, a secant crosses a curve, while a tangent just touches it at one point.

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