The standard form of a linear equation is expressed as
Ax + By = C
The given points that the line passed through are (6, 4) and (- 4, 9)
The first step is to find the slope of the equation. The formula for finding slope is expressed as
slope, m = (y2 - y1)/(x2 - x1)
From the points given,
x1 = 6, y1 = 4
x2 = - 4, y2 = 9
m = (9 - 4)/(- 4 - 6) = 5/- 10
m = - 1/2
The eqyation of a line in the slope intercept form is expressed as
y = mx + c
m = slope
c = y intercept
To find c, we would substitute m = - 1/2, x = 1 and y = 4 into the slope intercept equation. It becomes
4 = - 1/2 * 1 + c
4 = - 1/2 + c
c = 4 + 1/2 = 9/2
Thus, we have
y = - x/2 + 9/2
Converting it to standard form, the standard form is
x/2 + y = 9/2
- x + 2y = 9
where
A = - 1, B = 2 and C = 9