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 = ( yβ - yβ ) / ( xβ - xβ )
with (xβ, yβ ) = (7, - 3) and (xβ, yβ ) = (4, - 8)
m = = -
y = - x + c β is the partial equation
to find c substitute either of the 2 points into the partial equation
using (4, - 8 ), then
- 8 = - + c β c = -
y = - x - β in slope-intercept form
multiply all terms by 3 to eliminate the fractions
3y = - 5x - 4 ( add 5x to both sides )
5x + 3y = - 4 β in standard form