Question

Math

Posted 6 months ago

```
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) $\frac{\log (t)-\log (8)}{t-8}$
```

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Answer from Sia

Posted 6 months ago

Solution by Steps

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.

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