X+3y+9=0 and x+3y-7=0 are parallel or not ,how to work out,can anyone show me please
For any linear equation in the form
Ax + By + C = 0 , the slope is -A/B
So for both of your equations, the slope is -1/3
thus they are parallel
Thanks,now I totally understand
To determine if two lines are parallel, you can compare their slopes. If the slopes of the two lines are equal, then the lines are parallel.
To find the slope of a line in the form of Ax + By + C = 0, you can rearrange the equation into slope-intercept form (y = mx + b) by solving for y.
Let's solve both of the given equations for y in order to find their slopes:
Equation 1: x + 3y + 9 = 0
Rearrange the equation to isolate y:
3y = -x - 9
y = (-x - 9) / 3
y = -1/3x - 3
From the rearranged equation, we can see that the slope of this line is -1/3.
Equation 2: x + 3y - 7 = 0
Rearrange the equation to isolate y:
3y = -x + 7
y = (-x + 7) / 3
y = -1/3x + 7/3
From the rearranged equation, we can see that the slope of this line is also -1/3.
Since the slopes of both lines are equal (-1/3), we can conclude that the two lines are parallel.
In summary, to determine if two lines are parallel, compare their slopes. If the slopes are equal, then the lines are parallel. In this case, the slopes of the lines x + 3y + 9 = 0 and x + 3y - 7 = 0 are both -1/3, indicating that they are indeed parallel.