Question

Write an equation in point-slope form for the line through the given point with the given slope.

Answer 1

The required equation for the given point and the given slope is

`y+3=-(1)/(4)(x-8)`

Explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 8 ,-3)

`Slope = m =-(1)/(4)`

To Find:

Equation of Line Passing through A( x₁ , y₁) with slope = -1/4

Solution:

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,

i.e equation in point - slope form

`(y-y_(1))=m(x-x_(1))`

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 8 ,-3) we get

`(y-(-3))=-(1)/(4)(x-8)\\ \\y+3=-(1)/(4)(x-8)\ \textrm{which is the required equation in the option 2}`

The required equation for the given point and the given slope is

`y+3=-(1)/(4)(x-8)`