1) The standard form is a way to express a linear function as ax +by=c where a and b are the coefficients and c the number, or constant.
2) In our case, we have the equation given into the slope-intercept formula, so let's manipulate it algebraically
y=-3/2x +1 Subtract 1 from both sides
y-1=-3/2x +1 -1
-1+y =-3/2x Multiply by 2 on both sides
-2 +2y =-3x Add 3x, to both sides.
2 +2y+3x =-3x +3x Subtract 2 from both sides
3x +2y+2-2=-2
b) y = -5/3x -3
y = -5/3x -3 Add 3 to both sides
y+3 = 5/3x -3+3
y+3 = 5/3x Multiply both sides by 3
3(y+3) = 5x
3y+9 = 5x Subtract 9 from both sides
3y +9 -9= 5x -9
3y =5x -9 Subtract 5x from both sides
3y -5x = 5x -5x -9
3y -5x = -9
3x +2y = -2