From the January 2016 Common Core Geometry Regents
This is a graphing calculator question so into Y= we go.
Y1 = -1/2x -5 (the blue line) slope of -1/2 and y-intercept of (0,-5)
Then we will try all the choices until we find THE ANSWER!!
ok here we go…answer (1) into Y2 (see below)…um, not perpendicular, in fact, incredibly parallel as y = -1/2x + 4 also has a slope of -1/2
ok, ready for answer (2) into Y2? Here it is…looks mighty parallel (slope = -1/2)
onwards to Y3
So let’s look to see if the red line passes through (6,-4) it’s not there OK
and last but not least choice 4:
Now we have got it…we could also look at the table and see that (6,-4) is there>
We could also substitute in (6,-4) and see if it makes the equation(s) true
y = 2x -16
-4 = 2(6) – 16
-4 = -4 This makes the equation true — we kind of got lucky that (6,-4) does not make any of the other equations true.
This question can be extended with:
How slopes of parallel and perpendicular lines are related
Using these equations to demo systems of equations