Final answer:
The pair of lines defined by the equations 9x + 3y = 12 and 12x + 4y = 17 are parallel to each other because they both have the same slope of -3.
Step-by-step explanation:
To determine if the pair of lines defined by the equations 9x + 3y = 12 and 12x + 4y = 17 are parallel, perpendicular, or neither, we should convert each equation into slope-intercept form (y = mx + b). The slope-intercept form of a line reveals the slope (m), which determines the angle of the line relative to the axes, and the y-intercept (b), which is where the line crosses the y-axis.
For the first equation, 9x + 3y = 12, we can solve for y to get it in slope-intercept form:
For the second equation, 12x + 4y = 17, we again solve for y:
- 4y = -12x + 17
- y = -3x + 17/4
Both lines have the same slope of -3, which means they are parallel to each other and they are not perpendicular because perpendicular lines have slopes that are negative reciprocals of each other (in this case, one would need a slope of 1/3).