Tell whether the lines for the pairs of equations are parallel perpendicular or neither y equals negative 2/3 x + 1 2x - 3y = -3
To determine whether the lines represented by the given pairs of equations are parallel, perpendicular, or neither, we'll compare their slopes.
The equation y = (-2/3)x + 1 is already in slope-intercept form (y = mx + b), where m represents the slope. Therefore, we can directly identify that the slope of this line is -2/3.
Now, let's rearrange the equation 2x - 3y = -3 into slope-intercept form. Subtracting 2x from both sides, we get -3y = -2x - 3. Dividing both sides by -3 gives us y = (2/3)x + 1.
Comparing the equations, we see that both lines have slopes of -2/3. Hence, the lines represented by the given pairs of equations are parallel.