Find the equation of the line in standard form that passes through these points.

Question

(-9,-12) and (1,-3)

Answer 1

The equation of a line in Standard Form looks like this:    Ax + By = C

 

Now, you may go thru all the math of converting to slope-intercept form, or using two points with the point-slope form, or ,,,    or you may simply substitute what you already have.   

   slope = (y₂-y₁)/(x₂-x₁) = (-3-(-12))/((1-(-9)) = 9/10 = -A/B = A/(-B)

 

The equation is:  9x - 10y = C     and we need either point to find C

     9(1) - 10(-3) = C      [using point (1,-3)]

       39 = C

 

The equation of the line is:   9x -10y = 39

 

Check:

  Is (-9,-12) on the line?

      9(-9) - 10(-12) = 39   ?

        -81 + 120 = 39   ?

              39 = 39   ?yes

  Is (1,-3) on the line?

      9(1) - 10(-3) = 39   ?

       9 + 30 = 39   ?

           39 = 39   ?yes

 

Answer 2

[A] First, we must find the slope of the line. Since we were given 2 points (an x₁, x₂, y₁, and y₂ )  and no slope, we can rearrange the point-slope equation to find slope.

y-y₁=m(x-x₁) -->  m=(y₂-y₁) /(x₂-x₁) --> m=(-3--12)/(1--9) --> m=(-3+12)/(1+9) --> m=9/10

 

[B] Once we find slope, we can plug it into point-slope form along with one of the given points. Then we simply rearrange the equation into standard form (Ax + By = C).

 

y-y₁=m(x-x₁) --> y-(-3)=(9/10)(x-1) --> y+3=(9/10)(x-1)

 

[C] To remove the denominator, we multiply both sides by 10.

10(y+3)=10(9/10)(x-1)

10y+30=9(x-1)

 

[D] Then distribute 9 to remove the parenthesis.

10y+30=9x-9

 

[E] Now rearrange to the form Ax+By=C by moving 9x to the left side of the equal sign through subtraction, then move the 30 to the right side by subtracting it from -9.

-9x+10y=-39

 

*In step [C], there is another method to overcoming the fraction; instead of multiplying both sides by 10 at this step, you could also leave the fraction as-is, then rearrange the equation so the x value and y value are on the left side, THEN multiply each side by 10 to remove the fraction. Doing it this way yields -9x+10y=81-120. Doing the final bit of arithmetic on the right side gets you to the same answer. Use whichever method is easier for you to keep track of! I hope this helps =)

Answer 3

Hi Leah,

 

Find the equation of the line in standard form that passes through these points.
(-9,-12) and (1,-3)

 

The standard form of linear equation is Ax+By=C, where A,B and C are integers and A>0.

 

First we need to find the slope of the line

 

 

-3-(-12)

---------

1-(-9)

 

 

9/10 is the slope

 

y=mx+b

y=9/10x+b

 

To find the y-intercept substitute in either point.

 

I'm using point (1,-3)

 

-3=9/10(1)+b

-3=9/10+b

-39/10=b

 

so we have y=9/10x-39/10

 

to put in standard for  add -9/10x to both sides

-9/10x+y=-39/10

 

we're almost there...

since the coefficient must be integers and the A coefficient must be greater than zero, multiply the entire equation by -10.

 

-10[-9/10x+y=-39/10]

 

9x-10y=39

 

That's your answer.