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Question 1175149: Write the equation of a line that goes through the point (−8,2) and is parallel to the line 7x + 5y = 10 in slope-intercept form.
I have y = -7/5x + so far, I just cannot figure out the second part.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The other tutor paid no attention to the work you showed that you had done; they worked the problem in a completely different way that you might not know.
Let's look first at the method they were using, with some explanation. If you haven't seen this method yet in your studies, you almost certainly will. It is a useful method to know, because it often is less work than the method you are apparently trying to use.
You want the equation, slope-intercept form, of a line parallel to 7x+5y=10.
The basic principle the other tutor is using that any line parallel to 7x+5y=10 will have and equation of the form 7x+5y=C for some constant C.
So plug in the coordinates of the known point to find the value of C. Then convert the equation into slope-intercept form by solving for y:
7x+5y = C
7(-8)+5(2) = C
-56+10 = C
C = -46
7x+5y = -46
5y = -7x-46
y = (-7/5)x-46/5
Now let's finish the problem by the method you started with.
The line you are looking for has the same slope as the given line but a different y-intercept. So put the given equation in slope-intercept form, as you apparently did:
7x+5y=10
5y = -7x+10
y = (-7/5)x+2
You have found the slope you need; now you need to find the y intercept if the line with that same slope will pass through (-8,2). You know the equation will be of the form
for some value of b. To find that value of b, you again plug in the coordinates of the given point and solve the resulting equation, this time giving you the needed value of the y-intercept b.
The solution, of course, is the same as with the other method:
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