SOLUTION: write an equation of the line containing the given point and parallel to the given line (6,-8); 2x-9y=4

Question 145252: write an equation of the line containing the given point and parallel to the given line
(6,-8); 2x-9y=4
Found 2 solutions by nerdybill, Alan3354:
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
write an equation of the line containing the given point and parallel to the given line
(6,-8); 2x-9y=4
.
Remember, if a line is parallel to another, then their slope must be the same.
The problem wanted the line parallel to:
2x-9y=4
Rearrange the above to the "slope-intercept form" of:
y = mx + b
where
m=slope
b=y-intercept
.
2x-9y=4
-9y=-2x+4
y=(2/9)x-(4/9)
Now we know the slope of our line has to be 2/9.
Plug the "slope" we just found and the given point (6,-8) into:
y = mx + b
and solve for 'b':
-8 = (2/9)(6) + b
-8 = (12/9) + b
-8 = (4/3) + b
-24 = 4 + 3b
-28 = 3b
-28/3 = b
.
Therefore we now know TWO things for our new line:
slope = 2/9
y-intercept = -28/3
.
Your equation is therefore:
y = (2/9)x - (28/3)

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The slope of 2x-9y = 4 is 2/9. Slope m = -(Cx/Cy) where Cx is the coefficient of x and Cy is the coefficient of y. It's not necessary to do the y=mx+b, just use the 2 coefficients. The value on the right, 4 in this case, only moves the line up and down, it has no effect of the slope.
Now, we're looking for a line thru (6,-8) with a slope of 2/9 (parallel lines have the same slope).
-------------------
Now use m = (y2-y1)/(x2-x1)
Passing thru a point (X,Y), it's: y-Y = m(x-X)
y-(-8) = (2/9)(x-6)
y+8 = (2x-12)/9
9y+72 = 2x-12
9y+84 = 2x
2x - 9y = 84

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