Final answer:
The equations y = 5/4x + 1 and y = 5/4x - 7 are parallel to each other because they have the same slope, which is 5/4, but different y-intercepts.
Step-by-step explanation:
Determining the Relationship Between Two Linear Equations
To determine if the given equations y = 5/4x + 1 and y = 5/4x - 7 are parallel, perpendicular, or neither, we need to compare their slopes.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Both given equations are already in slope-intercept form:
- For the first equation, the slope m1 is 5/4.
- For the second equation, the slope m2 is also 5/4.
Since the slopes are equal and the y-intercepts are different, the two lines are parallel to each other.