Respuesta :

reinhard10158

Step-by-step explanation:

in what form do you need this equation ?

I simply assume it is the slope-intercept form :

y = ax + b

"a" is the slope of the line, "b" is the y-value when x = 0 (the point where the line intercepts the y-axis).

the slope is the ratio

y coordinate difference / x coordinate difference

when going from one point on the line to another.

in our case let's go from (2, 4) to (4, 2), as I personally prefer to go from left to right.

x changes by +2 (from 2 to 4).

y changes by -2 (from 4 to 2).

the slope is then -2/+2 = -1.

that means we know half of the equation :

y = -x + b

to get "b" we use the coordinates of one of the points in this half finished equation. e.g. (2, 4) :

4 = -(2) + b = -2 + b

b = 6

and our equation is

y = -x + 6
The answer is x + y - 6 = 0 (General Form)

EXPLANATION:

the formula to find the equation of a line is:
y - y1 = m(x - x1)

First, we need to find the gradient of points (4,2) & (2,4).
m = y2 - y1/x2 - x1

now sub them in: m = 4-2/2-4 = 2/-2 = -1
therefore m = -1

now pick a point and sub it into the equation of a line ( y-y1=m(x-x1)).

I will pick (4,2).

y - 2 = -1(x - 4)
y - 2 = -x + 4
now move x and 4 to the left side as x must always be positive in general form.
x + y - 6 = 0

ye