Question

Write the point-slope form of the equation of the line through the given point with the given

slope.
3) through: (1, -5), slope -5/6
4) through:(-2,5), slope = -7/2

Answer 1

Question 3)

Given

The point (1, -5)

The slope m = -5/6

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

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

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

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

`y-\left(-5\right)=-(5)/(6)\left(x-1\right)`

`y+5=-(5)/(6)\left(x-1\right)`

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

`y+5=-(5)/(6)\left(x-1\right)`

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

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

`y-5=-(7)/(2)\left(x-\left(-1\right)\right)`

`y-5=-(7)/(2)\left(x+1\right)`

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

`y-5=-(7)/(2)\left(x+1\right)`