Answer :
Given:
Parallel to line -9x - 4y = 30
y-intercept (0, -6)
To find:
The equation of a line parallel to given line
Solution:
Given line -9x - 4y = 30
Add 9x on both sides, we get
-4y = 9x + 30
Divide by -4 on both sides, we get
[tex]$y=\frac{-9x}{4}-\frac{30}{4}[/tex]
Slope of the given line is [tex]\frac{-9}{4}[/tex].
If two lines are parallel, then their slopes are equal.
Hence slope of the parallel line is [tex]\frac{-9}{4}[/tex].
y-intercept (0, -6)
c = -6
Equation of a line formula:
y = mx + c
Substitute the values.
[tex]$y=\frac{-9}{4}x-6[/tex]
The equation of a line parallel to given line is [tex]y=\frac{-9}{4}x-6[/tex].