You have got to love these questions.
KEY POINT: Parallel lines have equal slopes. Since the slopes are the same, the lines never intersect.
So what is the slope of your given line? Well, it helps that it is given in slope-intercept form so that you can read off the slope. The slope is the coefficient of the x term or the number by which x is multiplied. That would be 2 in this case.
Now we know that your parallel line will be of the format y = 2x + c. We just need to find c.
We do this by plugging in the x and y coordinates that you were given and then solving for c.
y = 2x + c
Your line has the point x=3 and y= 4 on it. So substitute those values into the equation.
4 = 2(3) + c
Do the multiplication:
4 = 6 + c
Isolate the c by subtracting each side by 6:
4 – 6 = 6 – 6 + c
–2 = c
Now go back to the equation that you are creating and fill in c to get:
y = 2x – 2
That is your answer.
