ANSWER
y = -2x + 4
Step-by-step explanation
a. We want to find the equation of the line that is parallel to the given equation and passes through (5, -6):
2x + y = 12
Let us put the equation in the slope-intercept form:
y = -2x + 12
When two lines are parallel, their slopes are equal.
The general form of a linear equation is:
y = mx + c
where m = slope
c = intercept
This means that the slope of the given equation is -2. Therefore, the slope of the equation we need is also -2.
Now, we can apply the point-slope method to find the equation of the line.
We have:
y - y1 = m(x - x1)
where (x1, y1) is a point that lies on the line
m = slope
(x1, y1) => (5, -6).
Therefore:
y - (-6) = -2(x - 5)
y + 6 = -2x + 10
=> y = -2x + 10 - 6
y = -2x + 4
That is the equation of the line that passes through (5, -6) and is parallel to the given equation.