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

To determine the value of q that makes the two lines 3y = 4x - 1 and qy = x + 3 parallel to each other, we need to remember that parallel lines have the same slope. The slope of the line 3y = 4x - 1 can be found by rearranging the equation into slope-intercept form, y = (4/3)x - 1/3, where the slope is 4/3. Similarly, the slope of the line qy = x + 3 is 1/q. For these two lines to be parallel, their slopes must be equal. Therefore, we can set 4/3 equal to 1/q and solve for q: 4/3 = 1/q q = 3/4 Therefore, the value of q that makes the two lines parallel is 3/4.