Slope

**Mr_Green** · January 27th 2007, 07:20 AM

If F(x) = 8^x contains the points A(a,3) and B(b,48), find the exact value of the slope of AB.

Could someone help me solve this please? It was on a practice SAT that I took, and I know I got it wrong cause I didn't know what to do.

Thanks

**earboth** · January 27th 2007, 08:57 AM

Originally Posted by Mr_Green

If F(x) = 8^x contains the points A(a,3) and B(b,48), find the exact value of the slope of AB.

Could someone help me solve this please? It was on a practice SAT that I took, and I know I got it wrong cause I didn't know what to do.

Thanks

Hello,

the coordinates of the points have to satisfy the equation of the function:

to A: $3=8^a \Longrightarrow a=\log_{8}{3}$

to B: $48=8^b \Longrightarrow b=\log_{8}{48}$

The slope is calculated by: $m=\frac{y_B-y_A}{b-a}$ Therefore:

$m=\frac{48-3}{\log_{8}{48}-\log_{8}{3}}=\frac{45}{\log_{8}{\left( \frac{48}{3} \right)}}$ = $\frac{45}{\frac{\ln{\left( \frac{48}{3} \right)}}{\ln(8)}}=\frac{45 \cdot \ln(8)}{\ln(16)}=\frac{45 \cdot 3\ln(2)}{4\ln(2)}=\frac{135}{4}$

EB

Thread: Slope

LinkBack

Thread Tools

Display

Slope

Similar Math Help Forum Discussions

Finding the slope of this function(the slope is also avg. velcoity I think)

slope

How to get a slope?

finding eq. of tan to the slope f(x) given the slope

Secant Line Slope and Tangent Line Slope

Search Tags