Find the value of k so that the line containing the points (−5,k) and (7,3) is parallel to the line containing the points (−8,−8) and (−1,−14)
slope = (-14+8)/(-1+8) = (3-k)/(7+5)
To find the value of k so that the line containing the points (-5, k) and (7, 3) is parallel to the line containing the points (-8, -8) and (-1, -14), we need to determine the slope of both lines and set them equal to each other.
The slope of a line can be calculated using the formula: slope = (y2 - y1) / (x2 - x1)
For the line containing the points (-5, k) and (7, 3), the slope is: (3 - k) / (7 - (-5))
For the line containing the points (-8, -8) and (-1, -14), the slope is: (-14 - (-8)) / (-1 - (-8))
Since the two lines are parallel, they have the same slope. Setting the slopes equal to each other, we get:
(3 - k) / (7 - (-5)) = (-14 - (-8)) / (-1 - (-8))
To simplify the equation, we can remove the negative signs:
(3 - k) / (7 + 5) = (-14 + 8) / (-1 + 8)
Simplifying further:
(3 - k) / 12 = (-6) / 7
Cross multiply:
7(3 - k) = 12(-6)
21 - 7k = -72
Re-arrange the equation:
-7k = -72 - 21
-7k = -93
Divide both sides by -7:
k = -93 / -7
k = 13.29 (rounded to two decimal places)
Therefore, the value of k that makes the line containing the points (-5, k) and (7, 3) parallel to the line containing the points (-8, -8) and (-1, -14) is approximately 13.29.
To determine the value of k that makes the line containing the points (-5, k) and (7, 3) parallel to the line containing the points (-8, -8) and (-1, -14), we need to compare the slopes of the two lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
First, let's calculate the slope of the line passing through the points (-8, -8) and (-1, -14):
slope1 = (-14 - (-8)) / (-1 - (-8))
= (-14 + 8) / (-1 + 8)
= -6 / 7
Now, let's calculate the slope of the line passing through the points (-5, k) and (7, 3):
slope2 = (3 - k) / (7 - (-5))
= (3 - k) / (7 + 5)
= (3 - k) / 12
Since the two lines are parallel, their slopes must be equal. Therefore, we have:
slope1 = slope2
Substituting the values of slope1 and slope2, we get:
-6 / 7 = (3 - k) / 12
To solve for k, let's cross-multiply:
-6 * 12 = 7 * (3 - k)
-72 = 21 - 7k
Rearranging the equation:
-7k = -72 - 21
-7k = -93
Dividing both sides by -7:
k = (-93) / (-7)
k = 13.3
Therefore, the value of k that makes the line containing the points (-5, k) and (7, 3) parallel to the line containing the points (-8, -8) and (-1, -14) is k = 13.3.
Find the value of k so that the line containing the points (-6,k)and (-3,4) is perpendicular to the line y=-5//6x-5.
K=??