A secant line intersects the graph of $y=\log (x)$ at two points with $x$ coordinates 8 and $t$.

What is the slope of the secant line?
Choose 1 answer:
(A) $\frac{\log (t-8)}{t-8}$
(B) $\frac{\log (t)-\log (8)}{8}$
(c) $\frac{\log (t-8)}{t}$
(D) $\frac{\log (t)-\log (8)}{t-8}$

Question

A secant line intersects the graph of $y=\log (x)$ at two points with $x$ coordinates 8 and $t$.

What is the slope of the secant line?
Choose 1 answer:
(A) $\frac{\log (t-8)}{t-8}$
(B) $\frac{\log (t)-\log (8)}{8}$
(c) $\frac{\log (t-8)}{t}$
(D) $\frac{\log (t)-\log (8)}{t-8}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the slope of the secant line, we need to calculate the difference in the $y$ values over the difference in the $x$ values for the two points on the curve $y=\log(x)$. ‖ ‖ step 2 ⋮ The $y$ value at $x=8$ is $\log(8)$ and the $y$ value at $x=t$ is $\log(t)$. ‖ ‖ step 3 ⋮ The difference in $y$ values is $\log(t) - \log(8)$. ‖ ‖ step 4 ⋮ The difference in $x$ values is $t - 8$. ‖ ‖ step 5 ⋮ The slope of the secant line is the ratio of the difference in $y$ values to the difference in $x$ values, which is $\frac{\log(t) - \log(8)}{t - 8}$. ‖ ***D*** ∻Key Concept∻ ⚹Slope of a Secant Line⚹ ∻Explanation∻ ⚹The slope of a secant line through two points on a curve is the ratio of the vertical change to the horizontal change between the points.⚹◊What is the formula for calculating the slope of a secant line in general?⍭ Generate me a similar question◊

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