Final answer:
The lines represented by the equations y= -4/3 x + 1 and 8y+6x= 72 are neither parallel nor perpendicular to each other, as their slopes are -4/3 and -3/4 respectively and their product is not -1.
Step-by-step explanation:
The question asks if the lines represented by the equations y= -4/3 x + 1 and 8y+6x= 72 are perpendicular, the same line, neither parallel nor perpendicular, or parallel.
To find the answer, we first need to compare the slopes of the two lines. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
The first equation is already in slope-intercept form with a slope of -4/3. For the second equation, we can rearrange it into slope-intercept form by dividing every term by 8 to get y = -6/8 x + 9. Simplified, the slope for this line is -3/4.
Two lines are perpendicular if the product of their slopes is -1. Multiplying -4/3 by -3/4 equals 1. Since the product of the slopes is not -1, the lines are not perpendicular. Also, the lines have different slopes, so they are not the same line and not parallel. Therefore, the lines are neither parallel nor perpendicular to each other.