If the lines 3y = 4x - 1 and qy = x + 3 are parallel to each other, the value of q is
Answer Details
Two lines are parallel if their slopes are equal. Slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.
The given lines are 3y = 4x - 1 and qy = x + 3. To find the slope of the first line, we can rearrange the equation in the slope-intercept form y = mx + b where m is the slope and b is the y-intercept.
3y = 4x - 1
y = (4/3)x - 1/3
So the slope of the first line is 4/3.
To find the slope of the second line, we can rearrange the equation in the same way:
qy = x + 3
y = (1/q)x + 3/q
So the slope of the second line is 1/q.
If the two lines are parallel, their slopes are equal. Therefore:
4/3 = 1/q
We can solve for q by cross-multiplying:
4q = 3
q = 3/4
Therefore, the value of q is 3/4.