Final answer:
To find the equation of a parallel line, use the same slope as the original line and apply it to the point-slope form with the given point. The resulting equation for the line parallel to 2x - y = 4 and passing through (-3, -11) is y = 2x - 17.
Step-by-step explanation:
To find the equation of a line that is parallel to another, we must ensure they have the same slope. The line given is 2x - y = 4. To find its slope, we can rewrite it in slope-intercept form (y = mx + b) by solving for y. The equation becomes y = 2x - 4. The slope (m) here is 2. Now, since parallel lines have equal slopes, our new line will also have a slope of 2.
Next, we use the point-slope form of a linear equation to find the equation of the line passing through the point (-3, -11) which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point. Substituting m with 2 and (x1, y1) with (-3, -11), we get y - (-11) = 2(x - (-3)), simplifying to y + 11 = 2(x + 3). Lastly, simplifying the equation we get y = 2x - 6 - 11, hence, the equation of the line is y = 2x - 17.