a line has the equation 2x + 5y = 7. another line passes through (3,6) and (k,9). what value for "k" will make the lines parallel?
please tell me HOW to do this, too!
thanks!
Parallel lines have the same slope.
9-6/k-3
3/k-3
The slope from the other must be
5y=7-2x
y= 7/5-2/5x
slope = -2/5
3/k-3=-2/5
15= -2 (k-3)
15= -2k+6
9= -2k
9/-2=k
To determine the value of "k" that will make the lines parallel, we need to consider the slopes of the two lines.
The given equation 2x + 5y = 7 can be rewritten in slope-intercept form (y = mx + b) by solving for y:
5y = -2x + 7
y = (-2/5)x + 7/5
The slope of this line is -2/5.
The second line passing through (3, 6) and (k, 9) can also be written in slope-intercept form. The formula to find the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the given points (3, 6) and (k, 9):
m = (9 - 6) / (k - 3)
m = 3 / (k - 3)
For these lines to be parallel, their slopes must be equal. Therefore, we set the slopes equal to each other and solve for "k":
-2/5 = 3 / (k - 3)
To get rid of the fraction, we can cross-multiply:
-2(k - 3) = 5 * 3
-2k + 6 = 15
-2k = 15 - 6
-2k = 9
k = 9 / -2
k = -4.5
So, the value of "k" that will make the lines parallel is -4.5.