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Question 3)

Given

The point (1, -5)

The slope m = -5/6

Using the point-slope form of the equation of a line

[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:

  • m = -5/6
  • (x₁, y₁) = (1, -5)

substituting the values m = -5/6 and the point (1, -5) in the point-slope form of the equation of the line

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

[tex]y-\left(-5\right)=-\frac{5}{6}\left(x-1\right)[/tex]

[tex]y+5=-\frac{5}{6}\left(x-1\right)[/tex]

Thus, the point-slope form of the equation of the line is:

[tex]y+5=-\frac{5}{6}\left(x-1\right)[/tex]

Question 4)

Given

The point (-1, 5)

The slope m = -7/2

In our case:

  • m = -7/2
  • (x₁, y₁) = (-1, 5)

substituting the values m = -7/2 and the point (-1, 5) in the point-slope form of the equation of the line

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

[tex]y-5=-\frac{7}{2}\left(x-\left(-1\right)\right)[/tex]

[tex]y-5=-\frac{7}{2}\left(x+1\right)[/tex]

Thus, the point-slope form of the equation of the line is:

[tex]y-5=-\frac{7}{2}\left(x+1\right)[/tex]

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