Expert: Chanda Walker - 12/29/2008

Question
Find the equation of the line which is parallel to the line with equation y-3x+5 and passes through the point with coordinates (4,10)

Answer
Hello Fawwaz,

For lines to be parallel, they must have equal slopes.  So the first thing we must do is find the slope of the original line.

The equation of that line is:

y - 3x + 5

Usually, an equation has an equal sign, that is the definition of an equation after all, so I'm going to assume that it equals zero.  Now, rearranging the equation we get:

y = 3x - 5

*IF* you accidentally mistyped that - minus when you meant an = sign, it is OK.  The answer, interestingly, will be IDENTICAL.  But let me know if you want to go through it again for that equation.

Since the equation for a line is y = mx + b, where m is the slope and b is the intercept, that means the slope must be 3 for the original line, and therefore for the new line too.  We now need to only find the intercept for the new line and we are finished.  To do that, we can substitute the point of the new line into the equation and solve for b.

new line:

y = 3 x + b

substitution:

10 = 3 * 4 + b

10 = 12 + b
-2 = b

Now that we know b, we are finished:

y = 3 x - 2

I hope this helps.  Let me know if this isn't clear enough.