What standard form line that passes through the point s(-1,4) and (-7,-5)

Question

What standard form line that passes through the points (-1,4) and (-7,-5)

Answer 1

We have two points (-1,4), (-7,-5)

As Michael J. said we can use the point slope formula

y - y₁ = m(x-x₁) where m is the slope and

(x₁, y₁) is a point on the line

 

m = (-5-4)/((-7-(-1)) = -9/-6 = 3/2

 

Let's use (-1, 4) as (x₁,y₁) with m=3/2

 

y - 4 = (3/2)(x-(-1))

y-4 = (3/2)(x+1)    multiply both sides by 2

 

2y-8 = 3(x+1)

2y-8 = 3x + 3

-3x + 2y = 11   or   3x - 2y = -11

 

 

Answer 2

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

 

For one line (with the same C as well as the same A and the same B) passing through these two points, that means:

    A(-1) + B(4) = C = A(-7) + B(-5) = C

       6A = -9B

 

So, let A=9 and B=-6 (note: this is just multiplying the entire equation by a constant):    9x-6y=D    [new constant D]

 

Choose either of the points:   9(-1)-6(4)=D

                     D=-33

 

The equation of the line, in Standard Format, that goes through (-1,4) and (-7,5) is:   9x-6y=-33

    Now, divide both sides by 3 to get:   3x-2y=-11

 

Checking (very important:

   Is    3(-1)-2(4) = -11   ?

             -11 = -11   ?yes

   Is    3(-7)-2(-5) = -11   ?

           -21+10  = -11   ?

               -11 = -11   ?yes

Answer 3

From the point-slope form of a line, we get

 

y - y₁ = mx - mx₁

 

 

If we manipulate this equation so that it is in standard form, we get

 

-mx + y = -mx₁ + y₁

 

 

where:

m is the slope between the two points

(x₁ , y₁) is any of the given points

 

All you have to do is find the slope.  Then pick any point given to you.  Plug in those values into the standard form of the line.