To find the slope of a line passing through two points (x1, y1) and (x2, y2), we can use the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, the points are (-2, 5) and (1, 4). Plugging the values into the formula:
slope = (4 - 5) / (1 - (-2))
slope = -1 / (1 + 2)
slope = -1 / 3
Therefore, the slope of the line passing through the points (-2, 5) and (1, 4) is -1/3.
A)
Multiple Choice
What is the slope of the line that passes through the points (–2, 5) and (1, 4)?
(1 point)
–3
–2
– 1/3
1/3
3 answers
A)
A line has slope – 5/3. Through which two points could this line pass?
(1 point)
(12, 13), (17, 10)
(16, 15), (13, 10)
(0, 7), (3, 10)
(11, 13), (8, 18)
A line has slope – 5/3. Through which two points could this line pass?
(1 point)
(12, 13), (17, 10)
(16, 15), (13, 10)
(0, 7), (3, 10)
(11, 13), (8, 18)
To find the points through which a line with a given slope passes, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is a point on the line.
In this case, the slope is -5/3. Let's use the first set of points, (12, 13) and (17, 10), and substitute into the point-slope form:
y - 13 = (-5/3)(x - 12)
y - 13 = (-5/3)x + 20
y = (-5/3)x + 33
Let's check if these points satisfy the equation:
For (12, 13):
13 = (-5/3)(12) + 33
13 = -20 + 33
13 = 13 --> satisfied
For (17, 10):
10 = (-5/3)(17) + 33
10 = -85/3 + 99/3
10 = 14/3 --> not satisfied
The line does not pass through the points (12, 13) and (17, 10).
Let's move on to the second set of points, (16, 15) and (13, 10):
y - 15 = (-5/3)(x - 16)
y - 15 = (-5/3)x + 80/3
y = (-5/3)x + 145/3
Let's check if these points satisfy the equation:
For (16, 15):
15 = (-5/3)(16) + 145/3
15 = -80/3 + 145/3
15 = 65/3 --> not satisfied
For (13, 10):
10 = (-5/3)(13) + 145/3
10 = -65/3 + 145/3
10 = 80/3 --> not satisfied
The line does not pass through the points (16, 15) and (13, 10).
Lastly, let's try the third set of points, (0, 7) and (3, 10):
y - 7 = (-5/3)(x - 0)
y - 7 = (-5/3)x + 0
y = (-5/3)x + 7
Let's check if these points satisfy the equation:
For (0, 7):
7 = (-5/3)(0) + 7
7 = 0 + 7
7 = 7 --> satisfied
For (3, 10):
10 = (-5/3)(3) + 7
10 = -15/3 + 21/3
10 = 6/3
10 = 2*3 --> not satisfied
The line does not pass through the points (0, 7) and (3, 10).
Lastly, let's try the last set of points, (11, 13) and (8, 18):
y - 13 = (-5/3)(x - 11)
y - 13 = (-5/3)x + 55/3
y = (-5/3)x + 94/3
Let's check if these points satisfy the equation:
For (11, 13):
13 = (-5/3)(11) + 94/3
13 = -55/3 + 94/3
13 = 39/3 --> not satisfied
For (8, 18):
18 = (-5/3)(8) + 94/3
18 = -40/3 + 94/3
18 = 54/3
18 = 2*3 --> not satisfied
The line does not pass through the points (11, 13) and (8, 18).
Therefore, the line with a slope of -5/3 does not pass through any of the given sets of points.
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is a point on the line.
In this case, the slope is -5/3. Let's use the first set of points, (12, 13) and (17, 10), and substitute into the point-slope form:
y - 13 = (-5/3)(x - 12)
y - 13 = (-5/3)x + 20
y = (-5/3)x + 33
Let's check if these points satisfy the equation:
For (12, 13):
13 = (-5/3)(12) + 33
13 = -20 + 33
13 = 13 --> satisfied
For (17, 10):
10 = (-5/3)(17) + 33
10 = -85/3 + 99/3
10 = 14/3 --> not satisfied
The line does not pass through the points (12, 13) and (17, 10).
Let's move on to the second set of points, (16, 15) and (13, 10):
y - 15 = (-5/3)(x - 16)
y - 15 = (-5/3)x + 80/3
y = (-5/3)x + 145/3
Let's check if these points satisfy the equation:
For (16, 15):
15 = (-5/3)(16) + 145/3
15 = -80/3 + 145/3
15 = 65/3 --> not satisfied
For (13, 10):
10 = (-5/3)(13) + 145/3
10 = -65/3 + 145/3
10 = 80/3 --> not satisfied
The line does not pass through the points (16, 15) and (13, 10).
Lastly, let's try the third set of points, (0, 7) and (3, 10):
y - 7 = (-5/3)(x - 0)
y - 7 = (-5/3)x + 0
y = (-5/3)x + 7
Let's check if these points satisfy the equation:
For (0, 7):
7 = (-5/3)(0) + 7
7 = 0 + 7
7 = 7 --> satisfied
For (3, 10):
10 = (-5/3)(3) + 7
10 = -15/3 + 21/3
10 = 6/3
10 = 2*3 --> not satisfied
The line does not pass through the points (0, 7) and (3, 10).
Lastly, let's try the last set of points, (11, 13) and (8, 18):
y - 13 = (-5/3)(x - 11)
y - 13 = (-5/3)x + 55/3
y = (-5/3)x + 94/3
Let's check if these points satisfy the equation:
For (11, 13):
13 = (-5/3)(11) + 94/3
13 = -55/3 + 94/3
13 = 39/3 --> not satisfied
For (8, 18):
18 = (-5/3)(8) + 94/3
18 = -40/3 + 94/3
18 = 54/3
18 = 2*3 --> not satisfied
The line does not pass through the points (11, 13) and (8, 18).
Therefore, the line with a slope of -5/3 does not pass through any of the given sets of points.
1 answer