The slope of a line whose equation is given in the form y=mx+k is m, that is, the coefficient of x.
We can rewrite x - 2y = 6 in the form y=mx+k as follows:
Add both sides 2y, and -6: the equation becomes x-6=2y.
Switching the sides, we get 2y=x-6. Finally, dividing by 2 we get:
y=(1/2)x-3.
Thus, the slope is (1/2).
Any line parallel to x - 2y = 6, must have slope equal to (1/2).
Thus, we want to write the equation of a line with slope 1/2, which passes through the point (-2, 4).
We achieve this as follows:
y-4=(1/2)(x-(-2)), that is y-4=(1/2)(x+2)
Expanding 1/2 over x, and 2, we have:
y-4=(1/2)x+1.
Finally, adding 4 to both sides, we get y=(1/2)x+5.
Answer: y=(1/2)x+5.
