How do I find the equation of a secant line using two given points?

In summary, the conversation revolves around finding the equation of a secant line with two given points, P[0,f(0)] and Q[3,f(3)]. The formula for calculating the slope of a secant line is mentioned, as well as the fact that a secant line is a straight line connecting two points. Ultimately, the equation y-f(0)=\frac{f(3)-f(0)}{3}(x-0) is derived as the solution to the problem.
  • #1
rocomath
1,755
1
Wow, someone asked me this question and I'm stumped.

Find the equation of the secant line that contain [tex]P[0,f(0)][/tex] and [tex]Q[3,f(3)][/tex]

Am I given enough information to solve this?

[tex]m=\frac{f(x+h)-f(x)}{h}[/tex]

...

[tex]m_1=\frac{f(h)-f(0)}{h}[/tex]

[tex]m_2=\frac{f(3+h)-f(3)}{h}[/tex]

That doesn't really help me though, unless I'm not thinking hard enough!
 
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  • #2
Isn't a secant line just a straight line with those two points?

uhm...

[tex]m=\frac{f(3)-f(0)}{3-0}[/tex]but the answer would be in terms of f(3) and f(0)
 
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  • #3
rock.freak667 said:
Isn't a secant line just a straight line with those two points?
Yeah and I'm given 2 points and I need to find an equation that contains both. Hmm.
 
  • #4
Oh I think I got it now, haha. My brain finally kicked in.
 
  • #5
rocophysics said:
Oh I think I got it now, haha. My brain finally kicked in.

What was it? Finding the equation of a line given two points? Or was my brain malfunctioning as well?
 
  • #6
rock.freak667 said:
What was it? Finding the equation of a line given two points? Or was my brain malfunctioning as well?
Yeah, seems like the only thing to do.

[tex]m=\frac{f(3)-f(0)}{3}[/tex]

[tex]y-f(0)=\frac{f(3)-f(0)}{3}(x-0)[/tex]

Not sure what else to think of.
 
  • #7
I would hope that is all there is to it.
 

1. What is the equation of a secant line?

The equation of a secant line is a linear equation that represents the average rate of change between two points on a curve or function. It is written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

2. How is the slope of a secant line calculated?

The slope of a secant line is calculated by finding the change in the y-values (rise) divided by the change in the x-values (run) between two points on a curve or function. This can be represented as (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

3. Can the equation of a secant line be used to find the slope at a single point?

No, the equation of a secant line can only be used to find the average rate of change between two points. To find the slope at a single point, the equation of a tangent line must be used.

4. How is the equation of a secant line used in calculus?

In calculus, the equation of a secant line is used to approximate the slope of a curve at a specific point. By taking the limit of the secant line as the two points get closer and closer together, the exact slope at that point can be found.

5. Can the equation of a secant line be used to find the area under a curve?

No, the equation of a secant line only represents the slope of a curve or function at two points. To find the area under a curve, the equation of a tangent line must be used in conjunction with integration.

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