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Write an equation in point-slope form for the line through the given point with the given slope. (-3,5); m=2/3

Respuesta :

absor201

Answer:

The equation in the point-slope form will be:

  • [tex]y-5=\frac{2}{3}\left(x-\left(-3\right)\right)[/tex]

Step-by-step explanation:

Given

  • point = (-3, 5)
  • slope = m = 2/3

Using the point-slope form of line equation

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

here

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

substituting the values m = 2/3 and the point (-3, 5)  in the point-slope form of the line equation

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

[tex]y-5=\frac{2}{3}\left(x-\left(-3\right)\right)[/tex]

Thus,  the equation in the point-slope form will be:

[tex]y-5=\frac{2}{3}\left(x-\left(-3\right)\right)[/tex]

NOTE: The equation in the point-slope can be further simplified such as:

[tex]y-5=\frac{2}{3}\left(x-\left(-3\right)\right)[/tex]

[tex]y-5=\frac{2}{3}\left(x+3\right)[/tex]

Add 5 to both sides

[tex]y-5+5=\frac{2}{3}\left(x+3\right)+5[/tex]

[tex]y=\frac{2}{3}x+7[/tex]

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