Question 145252
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)