The equation of Line 1 is y= 3x-2, and the equation of Line 2 is 5= 9x- 3y. Are the two lines parallel?

The equation of a line is given by the formula y= mx + c. Here, 'm' is the gradient of the line, and 'c' is the y intercept: where the line crosses the y axis. If two lines are parallel, then they must have the same gradient, as this means that they will never cross. Line 1 is already in the form y= mx + c, so first you should rearrange the equation for Line 2, changing it to 3y= 9x - 5 by adding 3y to both sides and subtracting 5 from both. As Line 1 has a gradient of 3, you should check if the equation for Line 2 can be simplified to give the same gradient. To do this, divide by 3, as this will leave you with just 'y' at the front. This will give the equation y= 3x - (5/3). We can now see that Line 1 is parallel with Line 2.