Find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6). (1 point)
m = 1
m = 2
m = –2
m = one-half***
8. Find the slope of a line that is perpendicular to the line containing the points (–2, –1) and (2, –3). (1 point)
m = –2
m = 2***
m = negative one over two
m = –1
Why did the parallel line bring a ruler to the party?
Because it wanted to measure up to the other lines!
So the correct answer is m = 2.
To find the slope of a line that is parallel to a given line, we can use the fact that parallel lines have the same slope.
Given the points (3, 4) and (2, 6), we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Substituting the values into the formula, we have:
m = (6 - 4) / (2 - 3)
m = 2 / -1
m = -2
Therefore, the slope of a line parallel to the line containing the points (3, 4) and (2, 6) is m = -2.
To find the slope of a line perpendicular to a given line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
Given the points (-2, -1) and (2, -3), we can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Substituting the values into the formula, we have:
m = (-3 - (-1)) / (2 - (-2))
m = (-3 + 1) / (2 + 2)
m = -2 / 4
m = -1/2
Therefore, the slope of a line perpendicular to the line containing the points (-2, -1) and (2, -3) is m = -1/2.
To find the slope of a line parallel or perpendicular to another line, we need to calculate the slope of the given line first. The slope of a line can be found using the formula:
m = (y2 - y1) / (x2 - x1)
For the first question, we are given the points (3, 4) and (2, 6). Let's substitute the coordinates into the formula:
m = (6 - 4) / (2 - 3)
m = 2 / -1
m = -2
The slope of the line containing the points (3, 4) and (2, 6) is -2.
For a line to be parallel to this line, it must have the same slope. So the answer is m = -2.
For the second question, we are given the points (-2, -1) and (2, -3). Let's substitute the coordinates into the formula:
m = (-3 - (-1)) / (2 - (-2))
m = (-3 + 1) / (2 + 2)
m = -2 / 4
m = -1/2
The slope of the line containing the points (-2, -1) and (2, -3) is -1/2.
For a line to be perpendicular to this line, it must have a negative reciprocal slope. The negative reciprocal of -1/2 is 2. So, the answer is m = 2.
parallel lines have the same slope
The line through (3, 4) and (2, 6) has slope (6-4)/(2-3) = -2
a perpendicular line has slope 1/2
The line through (–2, –1) and (2, –3) has slope -2/4 = -1/2
so a perpendicular line has slope 2
7 is 1/2
8 is -2