Question 6381: Find the equation of line which is perpendicular to the line y = x + 1 and passes the point (1,3)
I need HELP!!!!!! Thank you. If possible an immediate response would be greatly appreciated. Thank you again.
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Recall that perpendicular lines have slopes that are the negative reciprocal of each other.
What does this mean?
Well...if you know the slope of a line, then you automatically know the slope of all lines that are perpendicular to it. For example: If the slope of a line is m = (-3/5), then the slope of the perpendicular would be the negative reciprocal of (-3/5) which is +5/3
So, the given line has the slope, m = 1.
How do you know this? The given equation is in the slope-intercept form:
y = mx + b Compare this with:
y = x + 1 and you'll see that m (the slope) is 1.
Now your problem doesn't state which form of the equation is required so you could use the slope-intercept form or the point-slope form.
The point-slope form looks like this: y - y1 = m(x - x1) and this would be easier to write since you have all of the required information at hand and no calculations are necessary. The x1 and y1 are just the x and y values of the given point (1, 3)
Now, what is the slope of the new line? It's just the negative reciprocal of 1 which is -1.
Now we can write the equation of the line (in the point-slope form) that is perpendicular to given line (y = x + 1) and which passes through the given point (1, 3).
y - 3 = -1(x - 1)
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