Final answer:
After converting each equation to slope-intercept form, Lines 1 and 2 are found to be parallel with the same slope, and both are perpendicular to Line 3 as their slopes are negative reciprocals of each other.
Step-by-step explanation:
To determine whether the lines are parallel, perpendicular, or neither, we need to compare their slopes. Lines that are parallel have the same slope, while lines that are perpendicular have slopes that are negative reciprocals of each other. For the given equations, let's put them in slope-intercept form, y=mx+b, where m is the slope: Line 1: y=5/2x-6 (slope m1=5/2). Line 2: 2y=5x+7, which simplifies to y=5/2x+7/2 (slope m2=5/2). Line 3: 4x+10y=4, which simplifies to y=-2/5x+2/5 (slope m3=-2/5). Now let's compare the slopes of each pair of lines: Lines 1 and 2: m1=m2, so they are parallel. Lines 1 and 3: m1 * m3 = 5/2 * -2/5 = -1, so they are perpendicular. Lines 2 and 3 also have slopes that multiply to -1, so they are also perpendicular. In conclusion, Lines 1 and 2 are parallel, and each is perpendicular to Line 3.