Final answer:
To find the equation of the line parallel to 2y = 8x - 4 and passing through the point (-2,4), we first express the original line in slope-intercept form to identify the slope. The new line will have the same slope, which is 4. Substituting the slope and point into the slope-intercept form gives us the equation y = 4x + 12.
Step-by-step explanation:
The equation of the line that contains the point (-2,4) and is parallel to the line 2y = 8x − 4 can be found by first putting the given line into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. By dividing the whole equation by 2, we get y = 4x − 2. Since parallel lines have the same slope, the slope of our new line will also be 4. We then use the slope-intercept form again, substituting in our known slope and point to find the y-intercept, b, of the new line.
First, substitute the known point (-2,4) and slope (4) into the equation:
y = 4x + b.
Then:
4 = 4(-2) + b
4 = -8 + b
Adding 8 to both sides gives us:
b = 12.
Therefore, the equation of our new line is y = 4x + 12.