If the lines 3y = 4x - 1 and qy = x + 3 are parallel to each other, the value of q is

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.