# Thread: tangent/secant lines.

1. ## tangent/secant lines.

Am i supposed to just pick numbers for this?

Given the function y=(4/x)-6

a) Find two points that satisfy the function

b) Find the equation of the secant line through those two points.

c) Determine if there is a point of tangency where the tangent line is parallel to the secant line in part b). If there are such points, find them or show why such a point does not exist.

2. Originally Posted by JessicaWade
Am i supposed to just pick numbers for this?

Given the function y=(4/x)-6

a) Find two points that satisfy the function
Yep, pick 2 separate numbers for x, sub them in to find y

Originally Posted by JessicaWade

b) Find the equation of the secant line through those two points.
Use the points you found in part a to find the line $y = mx+c$

Do you know how to do this?

Originally Posted by JessicaWade

c) Determine if there is a point of tangency where the tangent line is parallel to the secant line in part b). If there are such points, find them or show why such a point does not exist.
Using the line from the previous part, pick out the gradient to help find a line that is parallel.

3. OK, so I picked x=2 & x=1 .. I don't know what to do for part B or C though.

4. What were your corresponding y ordinates for $x = 1,2$ ?

5. y = -4 & y = -2

6. Well done, now you have to find

$y = mx+c$

where $(x_1,y_1) = (1,-2)$ and $(x_2,y_2) = (2,-4)$

$
m = \frac{y_2-y_1}{x_2-x_1}
$