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Question 1078900: Find the equation of the line passing through the point P(2, - 1) and parallel to the line
y = 4x – 5. Write the equation in slope-intercept form.
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the equation of the line passing through the point P(2,-1) and parallel to the line y = 4x – 5.
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The slope, m, of y = 4x – 5 is 4.
Parallel lines have the same slope.
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Use y-y1 = m*(x-x1) where (x1,y1) is the given point.
Answer by ikleyn(52754)  (Show Source):
You can put this solution on YOUR website! .
Since the new line should be parallel to y = 4x-5, the new line has the equation
y = 4x + b (1)
with the same slope of 4 as the given line.
The parameter b in the last equation (1) in unknown for now.
You will find the value of this parameter by using the condition that the point P(2,-1) lies in this new line.
For it, simply substitute y= -1 and x= 2 into the equation (1). You will have
-1 = 4*2 + b. (2)
It is the equation for b. From this equation
b = -1 - 4*2 = -9.
So, the equation for the new line is
y = 4x -9. (3)
It has the same slope of 4, and pass through the point (2-1), since (x,y) = (2,-1) satisfies the equation (3):
-1 = 4*2 - 9.
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