Find the value of k so that the line containing the points (k,−8) and (−3,−5) is parallel to the line containing the points (9,7) and (12,5).
several of these have been done. Have you no input on this one?
To find the value of k such that the line containing the points (k,−8) and (−3,−5) is parallel to the line containing the points (9,7) and (12,5), we need to find the slope (m) of both lines.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's calculate the slope of the line passing through (9,7) and (12,5):
m1 = (5 - 7) / (12 - 9)
= -2 / 3
Since the line containing the points (k,−8) and (−3,−5) is parallel to the line containing the points (9,7) and (12,5), their slopes are equal:
m2 = -2 / 3
Now, using the formula for slope again, we can set up an equation to find the value of k:
m2 = (y2 - y1) / (x2 - x1)
-2 / 3 = (-5 - (-8)) / (-3 - k)
To simplify this, we can cross-multiply:
-2 (-3 - k) = -5 - (-8)
6 + 2k = -5 + 8
2k + 6 = 3
2k = 3 - 6
2k = -3
k = -3 / 2
Therefore, the value of k is -3/2 to make the line containing the points (k,−8) and (−3,−5) parallel to the line containing the points (9,7) and (12,5).