Line A is parallel to the line 4y+12x=24. Find the equation of Line A if it passes through the point (5,40/3).

Line A and line 4y+12x+24 are parallel. This means that they have the same gradient. In y=mx+c the gradient of the line is m. We can rearrange the equation 4y+12x+24 to find m. To begin with subtract 12x from both sides. This gives 4y=24-12x. Then divide both sides by 4. This gives y=6-3x. This tells us that the gradient of the line is -3, therefore the gradient of line A is also -3. We can now form the equation of the line A: y=-3x+c. To find the value for c we can place the coordinates which we were given in the question: 40/3=-3(5)+c. Multiply out the brackets to give: 40/3=-15+c. We can now find the value for c. Add 15 to both sides. This gives c=85/3. We can now form the equation for line A: y=-3x+85/3.