Final answer:
The equation of the line parallel to 2y + 4x = 12 and passing through (-4, 5) is y = -2x - 3. This was found by first getting the slope of the original line, which is -2, and then using the given point to find the y-intercept.
Step-by-step explanation:
To write the equation of a line that is parallel to 2y + 4x = 12 and contains the point (-4, 5), first, we need to find the slope of the given line. We rewrite the given equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Starting with 2y + 4x = 12, we can write:
- 2y = -4x + 12
- y = (-4x + 12) / 2
- y = -2x + 6
The slope (m) of the given line is -2. Since parallel lines have the same slope, the slope of our new line will also be -2.
Now that we have the slope, we use the point (-4, 5) to find the y-intercept (b) of our new line:
- 5 = -2(-4) + b
- 5 = 8 + b
- b = 5 - 8
- b = -3
Our equation is then y = -2x - 3, which is the equation of the line that is parallel to 2y + 4x = 12 and goes through the point (-4, 5).