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Question 989695: Given the equation y = 2x -7, write a linear equation in point slope form that is parallel to the line (5.1). Then change the equation to slope-intercept form.
I need to understand the steps and see the answer so I know how it was figured out. This will help me to finish all the other problems. Right now I don't know if what I come up with is accurate. Thank you! Keri and Logan
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'm assuming you meant to say "parallel to the line and it goes through (5,1)"
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Rule: Any two lines that are parallel have the same slope.
Using that rule above, we know that the parallel line has a slope of 2. This is because the slope of y = 2x-7 is 2 as well.
So m = 2 is the parallel slope
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The parallel line goes through (5,1) so x = 5 and y = 1.
We will plug m = 2, x = 5 and y = 1 into y = mx+b and solve for b
y = mx+b
y = 2x+b ... replace m with 2
y = 2*5+b ... replace x with 5
1 = 2*5+b ... replace y with 1, solve for b
1 = 10+b
1-10 = 10+b-10 ... Subtract 10 from both sides.
-9 = b
b = -9
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So we know that m = 2 and b = -9. Therefore the equation of the parallel line must be y = 2x - 9
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Edit: Point slope form is y - y1 = m(x-x1). The line goes through (5,1) so (x1,y1) = (5,1)
y - y1 = m(x-x1) turns into y - 1 = 2(x - 5) when you plug in the given info. So the equation of the line in point slope form is y - 1 = 2(x - 5)
The equation of the line in slope intercept form is y = 2x-9. This can be found by following the steps shown above or by solving for y in y - 1 = 2(x - 5)
Answer by josgarithmetic(39617) (Show Source):
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