Find a point-slope form for the equation of the line satisfying the conditions. Passing through (-9, -6) and (1, 1)

Question

Passing through (-9, -6) and (1, 1)

Answer 1

 ( -9, -6)    ( 1,1)

 

   This problem can be done in different ways . It is useful to know all those ways , so the property of equation of a line, linear relationship can be addressed

 

   We know that equation of a line is given by  Y = mx +b

 

     So , there are 2 parameters that should be determined:

    

     first m:

 

         1 - ( -6)  = 7

         1 - ( -9)    10 

 

        So our equation becomes:

 

         Y = 0.7 X + b

        Now, we plug the coordinate of any one of the 2 points to evaluate the b

 

         ( 1,1 )

 

        1 = 0.7 (1) + b

 

        b = 0.3

 

        Our equation of line becomes:

         

         Y = 0.7 X + 0.3

 

          If we use the other point we shoud get the same answer:

 

           ( -9, -6)

 

           - 6 = 0.7( -9) +b

 

              b = - 6 + 6.3 = 0.3

 

              then: Y = 0.7 X + 0.3

 

             Another method will be

 

            Y = mx + b

 

           Plug in coordinates of 2 point in the equation , and solve an equation with 2 variables.

 

              1 = m + b

              -6 = -9m + b

 

              1 - m = -6 + 9m

 

               10m = 7      m =.7 

 

                 1 = 0.7 + b

 

                  b = 0.3

 

             Y = 0.7X + 0.3

          

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Hi Keith;

(-9, -6) and (1, 1)

We first need the slope.  This is the change-of-y divided by the change-of-x...

(y-y₁)/(x-x₁)

(-6-1)/(-9-1)

-7/-10

A negative divided by a negative has a positive result...

7/10

Point-slope formula is...

y-y₁=m(x-x₁)

m is the slope.

Let's select one point to plug-in.  I randomly select the first...

y--6=(7/10)(x--9)

Subtracting a negative number is the same as adding a positive number...

y+6=(7/10)(x+9)

Let's distribute the 7/10...

y+6=[(7/10)(x)]+[(7/10)(9)]

y+6=(7/10)x+(63/10)

Let's convert the 6 into 10ths...

6=60/10

y+(60/10)=(7/10)x+(63/10)

Let's subtract 60/10 from both sides...

(-60/10)+y+(60/10)=(7/10)x+(63/10)-(60/10)

y=(7/10)x+(3/10)

Let's check our results with the other point, (1,1)...

1=(7/10)(1)+(3/10)

1=(7/10)+(3/10)

1=10/10

1=1