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The line CD passes through the points C (2.-1) and D (1, 1). Which of the
following represents the equation of the line in Point-Slope Form?*

Sagot :

absor201

Answer:

The equation of the line in Point-Slope Form will be:

[tex]y + 1 = -2(x - 2)[/tex]

Also, check the attached graph below.

Step-by-step explanation:

Given the points

  • C(2, -1)
  • D(1, 1)

Determining the slope between the points C (2.-1) and D (1, 1).

  • (x₁, y₁) = (2, -1)
  • (x₂, y₂) = (1, 1)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                =  [1 - (-1)] / [1 - 2]

               = [1+1] / [-1]  

               = [2] / [-1]

               = -2                    

Thus, the slope of the line = m = -2

The point-slope form of the line equation is defined as

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where

  • m is the slope of the line
  • (x₁, y₁) is the point

In our case:

  • (x₁, y₁) = (2, -1)
  • m = -2

substituting the values m = -2 and the point (x₁, y₁) = (2, -1) in the point-slope form of the line equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y - (-1) = -2 (x - 2)[/tex]

[tex]y + 1 = -2(x - 2)[/tex]

Therefore, the equation of the line in Point-Slope Form will be:

[tex]y + 1 = -2(x - 2)[/tex]

Also, check the attached graph below.

View image absor201
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