Question

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

Answer 1

The equation in the point-slope form will be:

• 
  `y-5=(2)/(3)\left(x-\left(-3\right)\right)`

Explanation:

Given

• point = (-3, 5)

• slope = m = 2/3

Using the point-slope form of line equation

`y-y_1=m\left(x-x_1\right)`

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

`y-y_1=m\left(x-x_1\right)`

`y-5=(2)/(3)\left(x-\left(-3\right)\right)`

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

`y-5=(2)/(3)\left(x-\left(-3\right)\right)`

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

`y-5=(2)/(3)\left(x-\left(-3\right)\right)`

`y-5=(2)/(3)\left(x+3\right)`

Add 5 to both sides

`y-5+5=(2)/(3)\left(x+3\right)+5`

`y=(2)/(3)x+7`