To compare the steepness of the slopes of different lines, we need to compare the absolute value of the coefficient of the x-term (the number in front of x) in each equation. A larger coefficient of x means a steeper slope, while a smaller coefficient of x means a less steep slope.
y = - 4 3 x + 2 3
The coefficient of x in this equation is - 4 3, this function has a steeper slope than the function y = - 3 2 x + 1 2
y = - 3 2 x + 1 2
The coefficient of x in this equation is - 3 2, this function has a steeper slope than the function y = - 2 x + 7 3
y = - 2 x + 7 3
The coefficient of x in this equation is - 2, this function has a steeper slope than the function y = - 7 4 x + 3 2
y = - 7 4 x + 3 2
The coefficient of x in this equation is - 7 4, this function has a steeper slope than the function y = - 8 7 x + 4 7
y = - 8 7 x + 4 7
The coefficient of x in this equation is - 8 7, this function has the least steep slope of all the functions.
So the order of the functions from steepest to least steep is: y = - 4 3 x + 2 3 , y = - 3 2 x + 1 2, y = - 2 x + 7 3, y = - 7 4 x + 3 2 , y = - 8 7 x + 4 7