Question

Write an equation in​ point-slope form of the line that passes through the given point and with the given slope m.

​(-4,1) m=4
The equation of the line is ?

Answer 1

An equation in​ point-slope form of the line that passes through the given point and with the given slope m = 4 will be:

`y-1 = 4(x-(-4))`

Explanation:

Given

• The point = (-4, 1)

• m = 4

Using the point-slope form of the line equation

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

here:

• m = slope

• (x₁, y₁) = point

substituting the values m = 4 and the point (-4, 1) in the point-slope form of the line equation

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

`y-1 = 4(x-(-4))`

Thus,

An equation in​ point-slope form of the line that passes through the given point and with the given slope m = 4 will be:

`y-1 = 4(x-(-4))`

Note: It can further be simplified

`y-1=4\left(x+4\right)`

Add 1 to both sides

`y-1+1=4\left(x+4\right)+1`

`y=4x+17`