Hello there. To solve this question, we'll have to remember some properties about equations of lines.
We start by solving the line equation given for y:
2x + 4y = 2
Subtract 2x on both sides of the equation
4y = 2 - 2x
Divide both sides by a factor of 4
y = 1/2 - x/2.
Knowing the line we want to find the equation passes through the point (2, 2) and it is parallel to the above line equation,
We know that when two lines are parallel, they share the same slope.
The slope of a line of the form y = mx + b is m.
In this case, that's why we solved for y, to find the equation in this form.
We can easily see that the slope of the first line is -1/2.
So, we have the equation of the line as:
y = -x/2 + b
To find the value of b, just plug in the coordinates of the point (2, 2):
2 = -2/2 + b
2 = -1 + b
Add 1 on both sides of the equation
b = 3
Therefore the equation is:
y = -x/2 + 3
The slope m is -1/2 and the y-intercept is b = 3.