SOLUTION: Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below. G (4, 6), H (1, 5)

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Question 1206891: Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below.
G (4, 6), H (1, 5)

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find slope. Write an equation for slope using either your point G or H, AND any unknown point (x,y). Adjust the form of your equation.

SLOPE:
%286-5%29%2F%284-1%29
cross%281%2F1%29
cross%281%29
slope should be 1%2F3.


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Choose points H and (x,y) for writing slope equation again.
H is at (1,5).

---removed---

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Indicate in standard form the equation of the line passing through the given points,
writing the answer in the equation box below.
G (4, 6), H (1, 5)
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        The solution in the post by @josgarithmetic is WRONG.
        It is incorrect from the first step calculating the slope and to the end,  including his answer highlight%28cross%28x-y=-4%29%29.
        I came to bring a correct solution. 


Calculate the slope m = increment_of_y_coordinate%2Fincrement_of_x_coordinate = %285-6%29%2F%281-4%29 = %28-1%29%2F%28-3%29 = 1%2F3.


It is the same as to use the formula  m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29  with coordinates  x%5B1%5D= 4,  y%5B1%5D= 6,  x%5B2%5D= 1,  y%5B2%5D= 5.



Next, write an equation of the line having the slope  1%2F3  and passing through the given point (4,6).


    An equation of a straight line in a coordinate plane which has the slope m and passes through the given point  P = (a,b)  is 

        y - b = m*(x-a).     

    Substitute here  m = 1%2F3,  a = 4,  b = 6,  and you will get

        y - 6 = %281%2F3%29%2A%28x-4%29.    (1)

    It is the equation in the slope-point form.

    But you want to get an equation in standard form, which is Ax + By = C.

    To get it, multiply equation (1) by 3 (both sides) and simplify

       3*(y-6) = x-4,

       -18 + 4 = x - 3y,

       -14 = x - 3y,

       x - 3y = -14.


This equation is what you want, i.e. your ANSWER.

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See the lesson
    - Equation for a straight line in a coordinate plane passing through two given points
in this site. Find there several other similar solved problems.

Learn the subject from there.


As a bonus to you,  consider the lessons in this site
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point
that are closely related to your problem.

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