the two lines have the same slope and different y-intercept, which means that the lines are parallel.
The lines are parallel, perpendicular, or neither?
Two linear equations:
y = a*x + b
y = c*x + d
Are parallel only if both have the same slope, which means that c = d, and the y-intercepts are different.
And are perpendicular if the slope of one of the lines is equal to the opposite of the inverse of the other slope, so:
a = -1/c
Now, our linear equations are:
3x + 2y = 6
y = (-3/2)*x + 5
We can write both of these in the slope intercept form:
3x + 2y = 6
2y = 6 - 3x
y = (6 - 3x)/2 = 3 - (3/2)*x
y = -(3/2)*x + 3
So the two lines have the same slope and different y-intercept, which means that the lines are parallel.
If you want to learn more about linear equations:
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