how can you tell in geometry that the equations are parallel, perpendicular , neither, either?
If the slopes of the lines are equal, the lines are parallel
if the slopes are negative reciprocals of each other, the lines are perpendicular, ( e.g. 5/3 vs -3/5)
parell is when lines are black
In geometry, you can determine whether two equations are parallel, perpendicular, neither, or either by examining their slopes. The slope of a line is a measure of how steep or slanted it is.
To compare the slopes of two lines, follow these steps:
1. Write the equations of the two given lines in slope-intercept form (y = mx + b), where "m" represents the slope.
2. Identify the slope of each line by comparing it to the coefficient of x in the equation. For example, if a line's equation is y = 2x + 3, its slope is 2.
3. Compare the slopes of the two lines:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals (multiplicative inverses) of each other (e.g., one slope is 2 and the other is -1/2), the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
- Note that if one or both of the slopes are undefined (e.g., x = 3 or y = 4), the lines may be vertical and are neither parallel nor perpendicular to any other line.
By comparing the slopes, you can determine the relationship between the given lines in terms of parallelism or perpendicularity.