Question

The point P(5,1) lies on the curve y=5x. If Q is the point (x,5x), find the slope of the secant line PQ for the following values of x. If x=5.1, the slope of PQ is:

Answer 1

Answer:

5

Step-by-step explanation:

We have been given that the point $P(1,5)$ lies on the curve $y=5x$. Q is the point $(x,5x)$. We are asked to find the slope of the secant line $PQ$ for $x=5.1$.

Let us find y-coordinate corresponding to $x=5.1$ for point P as:

$y=5(5.1)=25.5$

Now, we will use slope formula to find required slope.

$m=\frac{y_2-y_1}{x_2-x_1}$  

Let point $(1,5)=(x_1,y_1)$ and point $(5.1,25.5)=(x_2,y_2)$.

Using these points in slope formula, we will get:

$m_{PQ}=\frac{25.5-5}{5.1-1}=\frac{20.5}{4.1}=5$

Therefore, the slope of the line PQ is 5.