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

5

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=(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)=(25.5-5)/(5.1-1)=(20.5)/(4.1)=5`

Therefore, the slope of the line PQ is 5.