by HallsofIvy » Fri Jan 10, 2020 7:18 pm
Your English is excellent! Much better than my (insert pretty much any language here).
I would change the word order slightly: "Write the (equations for) the lines that are parallel and perpendicular to the line y= 2x+ 3 that pass through (1, 1)".
The slope of y= 2x+ 3 is 2. A line parallel to that also has slope 2 so has equation y= 2x+ b for some number b. What must b equal in order that this line pass through (1, 1)? A line perpendicular to that has slope -1/2 so equation y= (-1/2)x+ b for some number b. What must b equal in order that this line pass through (1, 1)?