1. 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 = 1/2


2. 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 = -2
m = –1

m = -2

m = 2

m is the change in y divided by the change in x.

So, for #1,
y changes from 4 to 6 (+2)
x changes from 3 to 2 (-1)
2/-1 = -2

To find the slope of a line that is parallel to a given line, you need to determine the slope of the given line first. The slope of a line can be calculated by using the formula:

m = (y2 - y1) / (x2 - x1)

Using the coordinates (3, 4) and (2, 6), we can substitute the values into the equation:

m = (6 - 4) / (2 - 3)
m = 2 / -1
m = -2

So, the slope of the given line is -2.

Since parallel lines have the same slope, the slope of any line parallel to the given line containing the points (3, 4) and (2, 6) will also be -2. Therefore, the correct answer for the first question is m = -2.

To find the slope of a line that is perpendicular to a given line, you need to determine the negative reciprocal of the slope of the given line. The negative reciprocal can be calculated by flipping the fraction and changing the sign.

Using the coordinates (-2, -1) and (2, -3), we can calculate the slope of the given line:

m = (-3 -(-1)) / (2 - (-2))
m = (-3 + 1) / (2 + 2)
m = -2 / 4
m = -1/2

The negative reciprocal of -1/2 is 2. Therefore, the slope of a line perpendicular to the line containing the points (-2, -1) and (2, -3) is 2. So, the correct answer for the second question is m = 2.