Question

What is the equation of a line that goes through the point (4, 2) and is parallel to the line given by the equation y = 2x + 6?

y = 4x - 6
y = -2x + 6
y = 2x - 6
y = -2x - 6

Answer 1

Parallel lines have equal gradients; the gradient is the coefficient of x.
In this case, it is very straight forward as there is only one equation in the list that has the same gradient/x-coefficient as the one in the question, which is 2.
The answer has to be the third option (y = 2x - 6) and sure enough, if you input the x-value 4 into the equation, you will get 2 as the y-value, so we know the line passes through the point (4, 2).

Answer 2

The answer is y=2x-6.