Answer:
y = 2x+ 7
Step-by-step explanation:
The equation y=3x-2 is in standard slope-intercept format of y=mx+b, where m is the slope and b is the y-intercept. Therefore, the slope of this given line is 2 (m=2). A parallel line will have the same slope, so lets write what we know so far about the new parallel line:
y = 2x+b
Any value of b will result in a line that is parallel to y=2x-2. But we need a value of b that will shift the line so that it goes through point (2,11). We can either do this by graphing to find what the value of b should be, or we can simply calculate it.
Calculate b by using the given point (2,11) and then solving for b:
y = 2x+b
11 = 2*(2)+b for (2,11)
11 = 4 + b
b = 7
The parallel line that goes through (2,11) is:
y = 2x+ 7
See the attached graph.