### Home > MC2 > Chapter 9 > Lesson 9.3.1 > Problem9-79

9-79.

Elyse, Paul and J'Marcus were looking at the graph below. Based on the graph, Elyse wrote the rule $y = 3x + 22$. Paul wrote the rule $y = 22x + 3$. J'Marcus wrote the rule $y = 22 + 3x$.

1. Are the three equations equivalent, or are they different? Explain your conclusion.

Look at the different parts of each equation. Is $3x$ the same as $3$? Is $22$ the same as $22x$?

Elyse and J'Marcus have the same equations because the terms can be switched around if they are related by addition.
$y = 3x + 22$
$y = 22 + 3x$
Paul's equation has a slope of $22$, because $22$ is the coefficient to $x$.
The equations that Elyse and J'Marcus wrote have a slope of only $3$, so Paul's equation is different.

2. Which equation (or equations) match the line on the graph? Justify your answer.

$\text{What is the } \frac{\text{rise}}{\text{run}} ?$

Find the slope of the line by picking two points on the line and making a slope triangle.
In the equations above, the slope is the coefficient of $x$.