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Math Help - Slope

  1. #1
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    Question Slope

    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
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    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
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