We will assume that the equation is a linear equation.
The general form of the linear equation is:
y = mx + c where:
m is the slope of the line and c is the y-intercept
(1) Calculating the slope (m):
The slope is calculated using the following rule:
m = (y2-y1) / (x2-x2)
The given points are: (12,10) which are represented by (x1,y1)
(24, 5) which are represented by (x2,y2)
Substitute with the givens in the above equation to get the slope as follows:
m = (5-10) / (24-12) = -5/12
(2) Calculating the y-intercept:
After getting the slope, the general equation can now be written as:
y = (-5/12) x + c
Any point belonging to this line would satisfy the equation. Therefore, to get the c, we will use any of the given points and substitute in the equation. The only unknown would be the c.
I will choose (12,10) to work with.
y = (-5/12) x + c
10 = (-5/12) (12) + c
10 = -5 + c
c = 10+5
c = 15
(3) Writing the complete equation:
Now, that the slope and y-intercept are calculated, the equation of the line can be written as follows:
y = (-5/12) x + 15
