Write the equation of a line that goes through the point ( 2, - 2 ) and is parallel to the line y = 2x - 11.

Step 1: Identify the slope of the given line The equation of the given line is in the form y = mx + b, where m is the slope. In this case, the slope of the line y = 2x - 11 is 2.

Step 2: Use the slope of the parallel line Parallel lines have the same slope. Therefore, the slope of the line we are trying to find is also 2.

Step 3: Use the point-slope form of a line The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We know that our line passes through the point (2, -2) and has a slope of 2, so we can substitute these values into the point-slope form:

y - (-2) = 2(x - 2)

Step 4: Simplify the equation Finally, we simplify the equation to put it in the slope-intercept form (y = mx + b):

y + 2 = 2x - 4 y = 2x - 6

So, the equation of the line that goes through the point (2, -2) and is parallel to the line y = 2x - 11 is y = 2x - 6.