Discovering the Slope of a Secant Line with Examples

[sasuke07]

Homework Statement

Find the slope of the line that joins P (0,2) and Q (x, 2^x+1) for x ≠0. type the expression using x as a variable.

Homework Equations

Rise over Run?

The Attempt at a Solution

I have a picture of the graph but i don't really know what to do, Please help.
I graphed it at x= -3, -2 and -1 cause that was part 1
Okay so i just had a thought in my mind. So we can use limits to find the slope of the secant line, So would i use The limit of 2^x+1 as x approaches 0. But then the slope would be 1, And how would i write the expression in terms of x.
So for when x=-1 the rise/run is .5/1
x=-2 rise over run is .75/2
and when x=-3 rise over run is .875/3
but now how would i do the expression part?

 

[jedishrfu]

need to show some work, why not compute the slope as you said rise over run

 

[bonfire09]

Just rewrite Q (x, 2^x+1) as Q(x)=2^x+1 and find your secant line at that point.

 

[SammyS]

Homework Statement

Find the slope of the line that joins P (0,2) and Q (x, 2^x+1) for x ≠0. type the expression using x as a variable.

Homework Equations

Rise over Run?

The Attempt at a Solution

I have a picture of the graph but i don't really know what to do, Please help.
I graphed it at x= -3, -2 and -1 cause that was part 1

Given two points on a line, do you know how to get the slope?

 

[sasuke07]

So for when x=-1 the rise/run is .5/1
x=-2 rise over run is .75/2
and when x=-3 rise over run is .875/3
but now how would i do the expression part?

 

[SammyS]

So for when x=-1 the rise/run is .5/1
x=-2 rise over run is .75/2
and when x=-3 rise over run is .875/3
but now how would i do the expression part?

Now find the slope for the line passing through points (0,2) and (x, 2^x+1 )

Yes, there will be a variable involved.

 

[sasuke07]

Now find the slope for the line passing through points (0,2) and (x, 2^x+1 )

Yes, there will be a variable involved.

couldn't i just use the limit of 2^x+1 as x approaches 0 to find the slope?

 

[SammyS]

couldn't i just use the limit of 2^x+1 as x approaches 0 to find the slope?

The slope of what?

 

[sasuke07]

the slope of the secant line

 

[sasuke07]

The slope of what?

doesn't the secant line connect those 2 points, so can't i figure out the slope using limits

 

[SammyS]

doesn't the secant line connect those 2 points, so can't i figure out the slope using limits

You don't need to take any limits. You're finding the slope of a line, given two distinct points, one of which has coordinates given in terms of x.

 

[sasuke07]

You don't need to take any limits. You're finding the slope of a line, given two distinct points, one of which has coordinates given in terms of x.

Thanks a lot for the help.
the answer was 2^x-1/x.