The equation in point-slope form is ?

Question

Find an equation in point-slope form for the line having the slope m=-6 and containing the point (7,9).

Answer 1

From the problem statement, we are given the slope "m=-6" and a point (7,9) on the line.  We will use the "point-slope" form to write the equation of that line...

 

(y-y₁)=m(x-x₁)....."point-slope" form

 (y-9)=(-6)(x-7)......substitute values for "m, x₁, y₁"

   y-9=-6x+42.......distribute (-6), RHS

   ∴ y=-6x+51.......add 9, both sides

 

So our equation in "point-slope" form is "y=-6x+51".

 

Let's check our work.  Substitute the point (7,9) back into our equation...

y=-6x+51........derived equation

9=(-6)(7)+51...substitute for "x, y"

9=-42+51.......simplify

9=9.................true, √check, our equation is

                        correct

 

Always check your solution and work!