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Question 423677: what is the equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?
please show steps to help me understand
Found 3 solutions by mananth, htmentor, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! -x-y = 4
Find the slope of this line
y=-x-4
Divide by 1
y=0.75x-4
Compare this equation with y=mx+b
slope m =0.75
The slope of a line parallel to the above line will be the same
The slope of the required line will be 0.75
m= 0.75 ,point (-5,1)
Find b by plugging the values of m & the point in
y=mx+b
1=-3.75 +b
b=4.75
m=0.75
The required equation is y=0.75x+ 4.75
Answer by htmentor(1343)  (Show Source):
You can put this solution on YOUR website! what is the equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?
Parallel lines have the same slope. Therefore, we know the equation has the form y = x + b. The only thing left to do is find the y-intercept. The slope of a line can be determined using two points on the line: m = (y2-y1)/(x2-x1).
Let's use the y-intercept as one of the points. Since x=0 at the y-intercept, we have:
m = 1 = (b-1)/(0 - -5). Solving for b gives (b - 1) = 5 -> b = 6.
So our equation is y = x + 6
Answer by ikleyn(53419)  (Show Source):
You can put this solution on YOUR website! .
what is  an equation of a line that passes through (-5, 1) and is parallel to y = x + 4 ?
please show steps to help me understand
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The solution in the post by @matanth is FATALLY WRONG and conceptually INCORRECT.
It contains arithmetic errors and does not satisfy the imposed conditions.
His line is not parallel to the given line.
I came to provide a correct solution.
Any line parallel to y = x + 4 has a form y = x + c with some constant 'c'.
The only thing is to determine the value of 'c'.
We use the given point (-5,1}: value of 'c' is determined by this equation y = x + c
after substituting coordinates of the point
1 = -5 + c,
c = 1 - (-5) = 1 + 5 = 6.
Answer. Equation of the line parallel to y = x+4 and passing through (-5,1) is y = x + 6.
Solved.
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