Question

Which equation is a point slope form equation for line AB ?

Answer 1

Option C

equation :
`y-5=(3)/(4) (x-6)`

Explanation:

Point slope form Equation states that the equation of a straight line in the form
`y-y_(1)=m(x-x_(1))`; where m is the slope of the line.

We have to find the equation for line AB.

From the figure, we have

The coordinate of
`A(x_(2) , y_(2))` = ( -2, -1) and
`B(x_(1) , y_(1))` = (6 ,5)

First find the value of m:

`m = (y_(2)-y_(1))/(x_(2)-x_(1))`

Now, substitute the points of A and B into slope m:

`m = (-1-(5))/(-2-(6))` or

`m =(-6)/(-8) = (3)/(4)`

Then, the equation of line:
`y-y_(1)=m(x-x_(1))`

Substitute the value of slope in above equation and the coordinates of
`(x_(1) , y_(1))` we have,

`y-5=(3)/(4) (x-6)`

Therefore, the equation for the point slope form is,
`y-5=(3)/(4) (x-6)`