Ax+By=C with (-7,7) and (-8,8)

Question

Find an equation of the line passing through the pair of points.  (-7,7) and (-8,8) 

Write equation in this form Ax+By=C 

Answer is  -15x +y=112

I don't know how to solve this.  Can someone help me

Answer 1

Mindy, I make lots and lots of typos.  I use the spelling checker; I have learned to have my work checked by others; and I concentrate on processes that reduce risk.  So, it was pretty easy for me to identify that the two points should be P₁ (-7,7) and P₂ (-8.-8).

The points are in the form (x,y) and they make the equation of the line TRUE.  That means that they are somewhere on the line described by the equation Ax+By=C.  This form of the equation of a line, Ax+By=C, is called the Standard Form.  There is also the Slope-Intercept Form, y=mx+b, and other forms.

 

So, the problem gives two points.  Two points determine a line.  That's why you can draw the line (and only one line) through those two points when you plot them.

 

Ready, let's find A, B, and C.    (It really is as easy as A,B,C,...)

 

The Standard Form of the equation of the line is:  Ax+By=C

(You may convert to slope-intercept form, but do it only once-and-forever) – the slope is:  -A/B

 

Given two points, P₁ and P₂, the slope is:  (y₂-y₁)/(x₂-x₁)= (-8-7)/((-8)-(-7)) = -15/(-1) = 15

        So,  -A/B = 15

 

The equation so far looks like:

       -15x + y = C             [note: multiples of this equation are the same line, so let A=-15, B=1]

 

Find the constant C by using either point.  Let’s use (-7,7):

     -15(-7) + 7 = C

         105 + 7 = C

          112 = C

 

There’s the equation:

    -15x + y = 112

 

Note:  The convention is to write the coefficient of x as positive, so multiply everything by (-1):

      15x – y = -112

Answer 2

slope=(8-7)/(-8-[-7])=1/-1=-1

y-8=-1(x-[-8]) point-slope form

y-8=-1(x+8)

y-8=-x-8

y=-x

x+y=0 is the equation, not the answer above

Answer 3

Hi Mindy, the first step is to find the slope of the line. The slope is given by the ratio:

 

y₁ - y₂ / x₁ - x₂

 

It does not matter which point is the (x₁, y₁) point. Either point will give the same answer.

 

Use (-7, 7) as the (x₁, y₁) point.

 

Slope:

 

(7 - 8) / (-7 - (-8)) = -1 / 1 = -1

 

The slope is -1.

 

Point-slope format of a line:

 

Using one of the two points and the slope, we can find the point-slope format of the line.

 

y - y₁ = m * (x - x₁)

 

This time we will use (-8, 8) as the point and the slope of -1:

 

y - 8 = -1 * (x - (-8))

 

y - 8 = -x - 8

 

Standard format of a line:

 

The standard format of the line is: Ax + By = C

 

Start with:

 

y - 8 = -x - 8

 

Add 8 to both sides of the equation:

 

y = -x

 

Add x to both sides of the equation:

 

x + y = 0

 

Answer:

 

x + y = 0

 

Mindy, your answer is not in the standard form. The x variable needs to be positive. If it was positive, you would have:

 

15x - y = -112

 

Additionally, neither of the points given will satisfy the equation for the line.