Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1: x=7
l2: y=7/9
The equation l1: x=7 represents a vertical line since the value of x is always 7, and the value of y can vary.
The equation l2: y=7/9 represents a horizontal line since the value of y is always 7/9, and the value of x can vary.
Since the lines are vertical and horizontal, they are perpendicular to each other.
To determine whether the two lines are parallel, perpendicular, or neither, we need to look at their slopes.
For line 1 (l1: x = 7), it is a vertical line. The equation describes a line where x is always equal to 7, and there is no slope. As such, line 1 is a vertical line with an undefined slope.
For line 2 (l2: y = 7/9), it is a horizontal line. The equation describes a line where y is always equal to 7/9, and the slope is 0.
Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals.
Since a vertical line has an undefined slope, it is neither parallel nor perpendicular to any other line.
Therefore, line 1 (l1: x = 7) and line 2 (l2: y = 7/9) are neither parallel nor perpendicular.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare their slopes.
For line l1: x = 7, it represents a vertical line where the x-coordinate is always equal to 7. The slope of a vertical line is undefined, as the denominator in the slope formula, (change in y)/(change in x), becomes zero.
For line l2: y = 7/9, it represents a horizontal line where the y-coordinate is always equal to 7/9. The slope of a horizontal line is zero since there is no change in the y-coordinate.
Since line l1 has an undefined slope and line l2 has a slope of zero, we can conclude that the two lines are perpendicular to each other.