Hello, Josephine,
The general form of an equation for a straight line is y = mx +b, where m is the slope and b is the y intercept (where the line crosses the y axis when x = 0). The slope is defined as the change in y as you change x. For lines to be parallel, they need to have the same slope. In this case, the slope of the line for y = 3x + 3 is "3." That is, when x increases by one, y increases by 3.
The parallel line, therefore, has the general form y = 3x + b. The only thing missing is "b." To find it, we know that the point (2,4) is on the second line, so let's use that point to calculate b. Do this by enering the data for x and y into the second equation:
y = 3x + b
4 = 3*2 + b
b = -2
The parallel line is therefore:
y = 3x - 2
Bob
