find the value of k if the interval joining the points (0,5) and (k,k+8) is parallel to the line 2x-4y-7=0
To find the value of k, we first need to determine the slope of the line passing through the points (0,5) and (k,k+8). The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
m = (y2 - y1) / (x2 - x1)
For the points (0,5) and (k,k+8), we have:
m = [(k+8) - 5] / [k - 0] = (k + 3) / k
Now, we know that a line parallel to the line 2x-4y-7=0 will have the same slope. The given line can be rewritten in slope-intercept form as:
4y = 2x + 7
y = (1/2)x + 7/4
The slope of this line is 1/2. Therefore, we have:
m = 1/2
Setting (k + 3) / k = 1/2:
(k + 3) / k = 1/2
2(k + 3) = k
2k + 6 = k
k = -6
Therefore, the value of k is -6.