slope intercept form of linear equation is y = mx + b where m is the slope and b is the y-intercept.
3x - 2y = 1 is the first equation.
subtract 3x from both sides to get:
-2y = -3x + 1
divide both sides of the equation by -2 to get:
y = (3/2)*x - (1/2)
slope for this equation is (3/2).
y - (2k + 1)*x = 3 is the second equation.
add (2k+1)*x to both sides to get:
y = (2k+1)*x + 3
slope for this equation is (2k+1)
if the lines are parallel, then their slopes are equal.
this means that:
2k+1 = (3/2)
subtract 1 from both sides of this equation to get:
2k = 1/2
divide both sides of this equation by 2 to get:
k = (1/4)
your answer should be k = (1/4)
substitute this value for k in the second equation.
second equation is:
y - (2k + 1)*x = 3
substitute k = (1/4) in this equation to get:
y - (2*(1/4) + 1)*x = 3
simplify to get:
y - (3/2)*x = 3
add (3/2)*x to both sides of this equation to get:
y = (3/2)*x + 3
your two equations are:
y = (3/2)*x - (1/2) (first equation)
y = (3/2)*x + 3 (second equation)
since they have the same slope, they are parallel to each other.
