Two lines have equations and 2x-3y+6=0 and 4x-6y+k=0
b. For what value of k will these lines be coincident?
since they are collinear of each other, would I just say k=12 because 2x doubled is 4x and -3y doubled is 6y and 6 doubled would be 12?
just so.
sorry? am I in the correct for thinking this?
"just so" means yes, you are correct.
sorry for my sophisticated language ...
To determine the value of k for which the two lines will be coincident (i.e., they will represent the same line), we need to ensure that their slopes are equal and their y-intercepts are also equal.
First, let's determine the slopes of the given lines. The slopes of the lines given by the equations 2x - 3y + 6 = 0 and 4x - 6y + k = 0 can be found by rearranging the equations into slope-intercept form (y = mx + b), where m represents the slope.
For the first equation: 2x - 3y + 6 = 0
Rearranging the equation, we get:
2x + 6 = 3y
(2/3)x + 2 = y
So, the slope of the first line is 2/3.
For the second equation: 4x - 6y + k = 0
Rearranging the equation, we get:
4x + k = 6y
(4/6)x + (k/6) = y
(2/3)x + (k/6) = y
So, the slope of the second line is 2/3.
Since the slopes of the two lines are equal, we need to determine the value of k such that their y-intercepts are also equal.
By comparing the y-intercepts of the two lines, we can equate the constants in both equations:
6 = k/6
Multiplying both sides by 6, we get:
k = 36
Therefore, for the two lines to be coincident, the value of k should be 36.