Write the standard form of the line that passes through the point (-2, 4) and is parallel to x - 2y = 6.

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.

 y=(1/2)x+5.