Question

I do I find the slope of AC and slope of the tangent line?

Answer 1

The slope of the radius is 2

The slope of the tangent line is -1/2

How to find the slope of the tangent line

The slope is represented as m, the slope by definition is the ratio change of the output values to the input values

Slope of the radius

Slope, m is calculated using the points on the graph (5, 2) and (6, 4)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values

m = (2 - 4) / (5 - 6)

m = (-2) / (-1)

m = 2

Slope of the tangent line

Points on the graph (7, 6) and (13, 3)

m = (y₀ - y₁) / (x₀ - x₁)

plugging in the values

m = (6 - 3) / (7 - 13)

m = (3) / (-6)

m = -1/2

Answer 2

Given:

Find-:

(A) Slope of radius

(B) Slope of tangent

Explanation-

The radius AB

Point A coordinates:

`\begin{gathered} A=(5,2) \\ \\ B=(7,6) \end{gathered}`

The formula of the slope is:

`m=(y_2-y_1)/(x_2-x_1)`

Where,

`\begin{gathered} (x_1,y_1)=\text{ First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}`

So, the slope of AB is:

`\begin{gathered} m=(6-2)/(7-5) \\ \\ m=(4)/(2) \\ \\ m=2 \end{gathered}`

The slope of the Radius is 2.

For the tangent line:

Take any two-point from a tangent,

`\begin{gathered} B=(7,6) \\ \\ C=(11,4) \end{gathered}`

The slope tangent is:

`\begin{gathered} m=(4-6)/(11-7) \\ \\ m=(-2)/(4) \\ \\ m=-(1)/(2) \\ \\ m=-0.5 \end{gathered}`

The slope of the tangent line is -0.5