Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1: x=4
l2: y=4/5
The equation l1: x = 4 represents a vertical line that passes through the point (4, y), where y can be any real number. This line is parallel to the y-axis.
The equation l2: y = 4/5 represents a horizontal line that passes through the point (x, 4/5), where x can be any real number. This line is parallel to the x-axis.
Since l1 is parallel to the y-axis and l2 is parallel to the x-axis, l1 and l2 are perpendicular to each other.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare their slopes.
For line 1 (l1), the equation is x = 4. Since there is no y-term, this means that the slope of this line is undefined. We can think of this line as a vertical line passing through x = 4.
For line 2 (l2), the equation is y = 4/5. Since there is no x-term, this means that the slope of this line is 0. We can think of this line as a horizontal line passing through y = 4/5.
Parallel lines have the same slope, so for the given lines to be parallel, their slopes must be equal. However, the slope of l1 is undefined, and the slope of l2 is 0.
Perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of l1 is undefined, it has no reciprocal. Therefore, we cannot determine the negative reciprocal of its slope. Consequently, it is not possible to determine if l1 and l2 are perpendicular.
In conclusion, the equations x = 4 and y = 4/5 do not represent parallel lines, perpendicular lines, or intersecting lines. They are simply a vertical line and a horizontal line intersecting at the point (4, 4/5).
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to examine their slopes.
For line l1: x = 4, this equation represents a vertical line that passes through the x-coordinate 4. The slope of a vertical line is undefined because the change in y is zero for any change in x.
For line l2: y = 4/5, this equation represents a horizontal line that passes through the y-coordinate 4/5. The slope of a horizontal line is zero because the change in y is zero for any change in x.
Since the slope of l1 is undefined, and the slope of l2 is zero, these lines are neither parallel nor perpendicular. They are simply two intersecting lines.