5x + 3y = - 4
step-by-step explanation:
the equation of a line in standard form is
ax + by = c ( a is a positive integer and b, c are integers )
express the line first of all in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)
m = 
= - 
y = - x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, - 8 ), then
- 8 = - 
+ c ⇒ c = - 
y = - x - ← in slope-intercept form
multiply all terms by 3 to eliminate the fractions
3y = - 5x - 4 ( add 5x to both sides )
5x + 3y = - 4 ← in standard form
