Answer:
equation in standard form is -3x + 5y = -26
Step-by-step explanation:
standard form of equation of line is
Ax + By = C
where A,B and C are integers.
such line has slope -A/B
Another form of line equation is slope intercept form, which can be written as
y = mx+ c
since in problem m = 3/5
thus, equation is
y = 3/5 x + c
Given that (2,-4) passes through this line, this point will satisfy the above equation
-4 = 3/5 *2 + c
=> - 4 = 6/5 + c
=> c = -4 -6/5 = (-4*5 - 6)/5
=> c = (-20 - 6)/5 = -26/5
Thus, equation in slope intercept form is
y = 3/5 x -26/5
lets rewrite this equation in Ax + By = C
Multiplying LHS and RHS by 5 we have
5y =( 3/5 x)* 5 - (26/5 * 5)
=> 5y = 3x - 26
we have to bring 3x on LHS for that
we subtract 3x from both side
5y -3x = 3x - 26 -3x
=> 5y -3x = - 26
rearranging the equation
-3x + 5y = -26
Thus, equation in standard form is -3x + 5y = -26
