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Question 124234: Help!!!! I am so confused with graphing..here is the question
What is the equation of a line parallel to y = -x + 3 through the point (2,4)
Can someone help?
Found 2 solutions by solver91311, Earlsdon:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Parallel lines have equal slopes, so if the line is parallel to  , then it must have the same slope.
Your equation is already in slope-intercept form. You know that because you have y on the left and everything else on the right. That means that the slope of the line is just the coefficient on x, and that is -1 in this case.
Now you need to create an equation of a line knowing the slope and one of the points. You use the point-slope form of the line to do this.
Point-slope form:  where  is the slope,  is the x-coordinate of the given point, and  is the y-coordinate of the given point.
For your problem:
Now all you have to do is substitute these values into the point-slope form
This result is a little messy, so you can either put it into standard form,  or slope-intercept form 
Standard form:
Slope-intercept form:
From the slope-intercept form you can see that this new line must be parallel to the given line because the slopes are both -1. You can check that this new line contains the given point by substituting the values of the coordinates into the new equation and check to see if these values result in a true statement.
 . This statement is clearly true, so the point (2,4) is on the line, and the answer checks.
Answer by Earlsdon(6294)  (Show Source):
You can put this solution on YOUR website! First, you want to write the new equation in the "slope-intercept" form (y = mx+b) unless instructed otherwise.
Second, recall that parallel lines have identical slopes, so if you know the slope of the line whose equation is given (y = -x+3), then you autmatically know the slope of any line parallel to this.
Compare the given equation which is already in the slope-intercept form with the general form:
y = -x+3
y = mx+b
You can see that the slope, m, of the given equation is -1.
So the slope of the new equation will be -1 because the new line is parallel to the given line.
Ok, now you can write the slope (m = -1) into the general equation:
y = -x+b
Now you need to find the value of b, the y-intercept.
You do this by substituting the x and y of the above equation with the x and y values taken from the given point (2, 4) through which the new line passes.
y = -x+b Substitute x = 2 and y = 4
4 = -2+b Add 2 to both sides.
6 = b This is the y-intercept of the new line so now you can write the final equation:
y = -x+6
I hope this clarifies the problem for you!
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