## Task

The figure below shows two lines. One is described by the equation $4x-y=c$ and the other by equation $y=2x+d$, for some constants $c$ and $d$. They intersect at the point $(p,q)$.

- How can you interpret $c$ and $d$ in terms of the graphs of the equations
above?
- Imagine you place the tip of your pencil at point $(p,q)$ and trace line $l$ out to the point with $x$-coordinate $p+2$. Imagine I do the same on line $m$. How much greater would the $y$-coordinate of your ending point be than mine?

## IM Commentary

This task requires students to use the fact that on the graph of the linear equation $y=ax+c$, the $y$-coordinate increases by $a$ when $x$ increases by one. Specific values for $c$ and $d$ were left out intentionally to encourage students to use the above fact as opposed to computing the point of intersection, $(p,q)$, and then computing respective function values to answer the question.

To see an annotated version of this and other Illustrative Mathematics tasks as well as other Common Core aligned resources, visit Achieve the Core.