I am not sure what the question is but i presume it means to prove if the two lines are parallel or not? In any case to prove 2 lines are parallel you must prove that the lines have the same gradient. A gradient is defined by the change of vertical height divided by change of horizontal distance. In maths it is presented by m (gradient) = delta y / delta x Alternately in a line for example y = 3x + 4 The co efficient of x is the gradient. Lines are usually written in the expression y = mx + c where m is the gradient and c is a constant. From the two equations you have stated first equation: x + 4y = 5 Easy way to find the gradient of this line is to arrange the equation in the form y = mx + c So taking x to the other side we get 4y = 5 - x Dividing by 4 y = 5/4 - x/4 therefore y = -x/4 + 5/4 From this we can see the co efficient of x is -1/4 which is the gradient of this line. equation 2 -3x = 12y - 13 Taking 13 to the other side 12y = -3x + 13 dividing by 12 y = - 3x / 12 + 13 /12 Cancelling 3/12 can be written as 1/4 therefore y = -x/4 + 13/12 so the gradient of this line is -1/4. Since the gradients are equal we can say the both equations give parallel line. ANOTHER WAY TO SOLVE There is an alternat method to find the gradeint. The formula to do is gradient = change of vertical distance / change of horizontal distance. For this you need 2 co ordinates for each equation and using the formula m = y2 - y1 / x2 - x1 Where m is the gradient (x1, y1) and (x2, y2) are co ordinates of two points in the line. Since only the equation is given u need to find these co ordinates for each equation. Equation 1 x+4y = 5 If we take x = 1 then 4y = 5 - 1 y = 4 /4 y = 1 So the first co ordinates are (1,1) If we take x = -3 4y = 5 + 3 y = 8/4 y = 2 So your 2nd co ordinatse are (-3,2) Using these values for m = y2 - y1 / x2 - x1 m = 2-1 / -3 - 1 m = - 1/4 Which gives the same value for the gradient. similarly for equation 2 if you put in 2 values of x and find two values of y. substitue into the equation to find the gradient you will get the same result. Hope this helps and im not sure what the question was so i guessed it. sorry if it is not relevant to what you wanted to know.