Question

rule of four: multiple representations of mathematics
create a table

p	c
5	25
7	35
9	45
10	50

graph

expression/equation

words
label graph.
describe the pattern in the graph.
check your expression/equation

Explanation:

Step1: Identify the relationship

Check ratio of $c$ to $p$: $\frac{15}{3}=5$, $\frac{25}{5}=5$, $\frac{35}{7}=5$, $\frac{45}{9}=5$, $\frac{50}{10}=5$

Step2: Write the equation

Since $c = 5p$ for all pairs

Step3: Verify the equation

Substitute $p=3$: $c=5\times3=15$; $p=10$: $c=5\times10=50$, matches table values.

Step4: Describe graph pattern

Plot points $(3,15),(5,25),(7,35),(9,45),(10,50)$; they form a straight line passing through the origin, with slope 5.

Answer:

EXPRESSION/EQUATION:

$c = 5p$

GRAPH:

(Plot the points $(3,15)$, $(5,25)$, $(7,35)$, $(9,45)$, $(10,50)$ on a coordinate plane with the horizontal axis labeled $p$ and vertical axis labeled $c$. Draw a straight line through these points starting at the origin.)

WORDS:

The graph is a straight, upward-sloping line passing through the origin. As the value of $p$ increases by 1, the value of $c$ increases by 5, showing a proportional linear relationship.

CHECK YOUR EXPRESSION/EQUATION:

Substituting each $p$ value from the table into $c=5p$ yields the corresponding $c$ value exactly, confirming the equation is correct.