Find the slope of the lines that are (a) parallel lines (b) perpendicular lines to the lines passing through the pair of points (3, 4)(2,-1)
y2-y1 /x2-x1
-1-4/ 2-3
m = -5/-1
m = 5
parallel = slope 5
perpendicular slope -1/5
slope with the given points
= (-1-4)/2-3) = -5/-1 = 5
so any parallel line has slope 5
any perpendicular line has slope -1/5
To get the slope we use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1,y1) and (x2,y2) are the points.
Substituting,
m = (4 - (-1)) / (3 - 2)
m = (4 + 1) / 1
m = 5
(a) Note that parallel lines have equal slope. Thus slope of the parallel line is also equal to 5.
(b) Note that perpendicular lines have negative reciprocal of slope of each other. Thus, the slope of perpendicular line is equal to -1/5.
Hope this helps :3
To find the slope of lines parallel or perpendicular to a given line passing through a pair of points, we can follow these steps:
Step 1: Find the slope of the line passing through the given pair of points (3, 4) and (2, -1).
The slope of a line between two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (3, 4) and (2, -1), we can substitute the values:
slope = (-1 - 4) / (2 - 3) = (-5) / (-1) = 5
So, the slope of the line passing through the points (3, 4) and (2, -1) is 5.
Now, let's move on to finding the slopes of parallel and perpendicular lines.
(a) Parallel Lines:
Parallel lines have the same slope. Therefore, the slope of any line parallel to the given line passing through the points (3, 4) and (2, -1) will also be 5.
(b) Perpendicular Lines:
The slopes of perpendicular lines are negative reciprocals of each other. We can find the slope of a line perpendicular to the given line by taking the negative reciprocal of the slope of the given line.
The negative reciprocal of 5 can be found by flipping the fraction and changing its sign.
Negative reciprocal of 5 = -1/5
Therefore, the slope of any line perpendicular to the given line passing through the points (3, 4) and (2, -1) will be -1/5.
In summary:
(a) The slope of parallel lines is 5.
(b) The slope of perpendicular lines is -1/5.