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

Substitution

Using these equations to demo systems of equations