# Applying our skills with lines

Grade 9s worked backwards today, given the graph of several lines, they determined the equations based on the constant, and the rate.

Their challenge then was extended to create lines that were parallel or perpendicular to the given lines. We’d seen parallel lines before and knew that they have the same slope. We have a call and repeat chant “parallèle” “même pente” that we have engrained in our long term memory.

Some of these lines were tricky since we couldn’t read the constant on the graph, we needed to use our reasoning skills to determine the equation.

Our new chant of the day is “perpendiculaire” “inverse négative” which means we take the slope of one line and flip the fraction, and multiply by negative 1. In English that is called the “negative reciprocal”.

The second equation is perpendicular to the first, and also direct.

We looked a little at different ways of managing if the line doesn’t look like y=mx+b. We can either do some algebra to isolate y, or we can use the x and y intercepts to graph the line.

Here’s the algebra to isolate y.

And here’s how we can find the intercepts. We know that the equation of the x axis is y=0, and the equation of the y axis is x=0 so we sub x=0 and solve for y, and also y=0 and solve for x.

We can see how all of this makes sense on the graph

Busy day today learning a lot!