Answer:
The equation of line passing through point ( - 2 , 4) with slope parallel to given line is y =
x + 5
Step-by-step explanation:
Given as :
The equation of line is x - 2 y = 6
Or, 2 y = x - 6
Or, y =
× x - ![\dfrac{6}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B2%7D)
i.e y =
× x - 3
<u>Now, Standard equation of line in slope-intercept form </u>
y = m x + c
where m is the slope of line
And c is the y-intercept
Now, Compare given line with standard line equation
So, The slope of line y =
× x - 3 = m =
<u>Again</u>
Other line is passing through points ( - 2 , 4) and is parallel to given line
∵ For parallel lines condition
The slope of both lines are equal
Let The slope of other line = M
So, from condition
M = m =
<u>Now, equation of line passing through point ( - 2 , 4) with slope
</u>
So, Equation of line in slope-point form
y -
= M × (x -
)
Or, y - 4 =
× (x - ( - 2) )
Or, y - 4 =
× (x + 2 )
Or, y =
× (x + 2 ) + 4
Or, y =
× x +
× 2 + 4
Or, y =
× x +
+ 4
∴ y =
× x + 1 + 4
i.e y =
x + 5
So, Equation of other line y =
x + 5
Hence, The equation of line passing through point ( - 2 , 4) with slope parallel to given line is y =
x + 5 . Answer