SOLUTION: I don't understand how to do this equation. The equation question is "write an equation of the line through the point (4,-2) that is parallel to the line -5x+6y=-2?"

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Question 880335: I don't understand how to do this equation. The equation question is "write an equation of the line through the point (4,-2) that is parallel to the line -5x+6y=-2?"
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The line containing (4,-2) and parallel to -5x+6y=-2 will have the same slope but a different constant.

Assuming you do not understand Standard Form, convert the given equation into slope-intercept form:
6y=5x%2B%28-2%29
y=%285%2F6%29x-2%2F6
y=%285%2F6%29x-1%2F3
... and the slope you want is highlight_green%28highlight_green%285%2F6%29%29.

Let us put that back into the equation we want to find, and change back from slope-intercept form to standard form.
y=%285%2F6%29x%2Bb, because at this point we do not know the y-intercept
y-%285%2F6%29x=b
-%285%2F6%29x%2By=b
-5x%2B6y=6b,
This is back into standard form, but we want to know what is the value of 6b.

Substitute the point which is supposed to be contained on this line, the given point (4,-2) and compute 6b. You do not need to solve for b here; you only want the value of 6b as the combined constant.
-5%284%29%2B6%28-2%29=6b
-20-12=6b
highlight_green%286b=-32%29
-
The use of "b" is for the y-intercept in the slope-intercept equation form. In this specific problem example, we need 6b for the standard form equation.
Finally our wanted equation is highlight%28-5x%2B6y=-32%29.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the given line
+-5x+%2B+6y+=+-2+
+6y+=+5x+-+2+
+y+=+%285%2F6%29%2Ax+-+1%2F3+
This is in the form +y+=+m%2Ax+%2B+b+
where +m+ = slope, so
+m+=+5%2F6+
Any line parallel to this line will
have the same slope
---------------------------------------
given the point (4,-2)
Use the general point-slope formula
+%28+y+-%28-2%29+%29+%2F+%28+x+-+4+%29+=+5%2F6+
+y+%2B+2+=+%285%2F6%29%2A%28+x+-+4+%29+
+6%2A%28+y+%2B+2+%29+=+5%2A%28+x+-+4+%29+
+6y+%2B+12+=+5x+-+20+
+5x+-+6y+=+32+ answer
---------------------
check:
does it go through (4,-2) ?
+5x+-+6y+=+32+
+5%2A4+-+6%2A%28-2%29+=+32+
+20+%2B+12+=+32+
+32+=+32+
OK