Parallel and Perpendicular

We’ve been working a lot with lines since coming back from the break.  We already looked at parallel lines a while back.  We know they don’t cross each other, and they run like train tracks always separated by the same distance.  We now can identify that they are increasing or decreasing at the same rate, or they have the same slope (“même pente”)….in fact we have been doing lots of chanting out loud… when someone say “parallèle” the response is “même pente”, and most of us have this word association stuck in our minds.

We know that the slope is the coefficient of x when the equation is written with y isolated.  This is the y=mx+b form.  The b value is the constant, the initial value, the y intercept (“ordonnée à l’origine”).  

We learned that perpendicular lines intersect, and always form a 90 degree angle.  If one slope is positive the other is negative, if one slope is 0 the other is undefined (indéfinie).  If one slope is steep, the other is not.  That’s the only way they’ll have a 90 degree angle between them.

The slopes are related.  This example has one slope of 1/2 and the other of -2/1.   The fraction is inverted, and one is positive and the other is negative.  We determined a process for finding a perpendicular slope is to invert the fraction and to multiply by negative 1.  Our chanting and word association continued, and when someone says “perpendiculaire” the response is “inverse négative”, the rhythm is a bit catchy.  

We see the slopes as the x coefficients again, when y is isolated.