Question

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

Answer 1

Answer:

Option C

equation :  $y-5=\frac{3}{4} (x-6)$

Step-by-step 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:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

$m = \frac{-1-(5)}{-2-(6)}$ or

$m =\frac{-6}{-8} = \frac{3}{4}$

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,

$y-5=\frac{3}{4} (x-6)$

Therefore, the equation for the point slope form is, $y-5=\frac{3}{4} (x-6)$