Answer:
The equation of other line parallel to given line is y = [tex]\dfrac{x}{2}[/tex] + 5 .
Step-by-step explanation:
Given as :
The equation of a line is
x - 2 y = 6
Or, 2 y = x - 6
Or, y = [tex]\dfrac{1}{2}[/tex]x - [tex]\dfrac{6}{2}[/tex]
i.e y = [tex]\dfrac{1}{2}[/tex]x - 3
The standard equation of line is given as
y = m x + c
where m is the slope of line
Now, comparing given line with standard line equation
The slope of line x - 2 y = 6 is m = [tex]\dfrac{1}{2}[/tex]
Again
Other line is passing through point (- 2 , 4) and is parallel to given line
For parallel line condition
slope of both lines are equal
Let The slope of other line = M
So, M = m = [tex]\dfrac{1}{2}[/tex]
Again
Equation of line with slope [tex]\dfrac{1}{2}[/tex] and passing through point (-2 , 4)
y - [tex]y_1[/tex] = M ( x - [tex]x_1[/tex] )
i.e y - 4 = ([tex]\dfrac{1}{2}[/tex]) ( x + 2)
Or, y - 4 = [tex]\dfrac{x}{2}[/tex] + 1
Or, y = [tex]\dfrac{x}{2}[/tex] + 1 + 4
i.e y = [tex]\dfrac{x}{2}[/tex] + 5
Hence, The equation of other line parallel to given line is y = [tex]\dfrac{x}{2}[/tex] + 5 . Answer
