determine whether the graphs of the following equations are parallel or perpendicular y=2/3x + 3, y=3/2x, 2x-3y=8
To determine whether the graphs of two lines are parallel or perpendicular, we need to compare their slopes.
For the first pair of equations:
y = (2/3)x + 3
y = (3/2)x
The slope of the first equation is 2/3, and the slope of the second equation is 3/2. Since the product of these slopes is equal to -1, the lines are perpendicular to each other.
For the second pair of equations:
2x - 3y = 8
To determine the slope of this equation, we need to write it in slope-intercept form (y = mx + b), where m is the slope.
Let's rearrange the equation:
-3y = -2x + 8
Divide both sides by -3:
y = (2/3)x - 8/3
The slope of this equation is 2/3.
Since the slope of the second equation, 2x - 3y = 8, is also 2/3, the lines are parallel to each other.
In summary, the graphs of the equations y = (2/3)x + 3 and y = (3/2)x are perpendicular, while the graph of the equation 2x - 3y = 8 is parallel to the graph of y = (2/3)x - 8/3.
check the slopes. If they are all the same, then the lines are parallel.
If their product is -1 (as with -4 and 1/4) then the lines are perpendicular.