As a seismologist, Janet understands the devastating effects that earthquakes can have. so, she keeps her basement stocked with canned food, like chili. This table shows the relationship between the number of cans of chili Janet buys, x, and the total cost (in dollars), y.
[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]
According to the values in the table, x and y have not a proportional relationship.
Table
[tex]\begin{tabular}{|c|c|c|}\underline{x(cans)}&\underline{y(dollars)} \\12 & \$\ 26.40 \\ 44 & \$\ 56.80 \\ 66 & \$\ 77.70 \\ 100 & \$\ 110 \end{align}[/tex]
Specifies the gradient (m) in rows 1 and 2
m₁ = [tex]\displaystyle \frac{56.80 - 26.40}{44-12}[/tex]
m₁ = [tex]\displaystyle \frac{30.40}{32}[/tex]
m₁ = [tex]\displaystyle \frac{19}{20}[/tex]
Specifies the gradient (m) in rows 2 and 3
m₂ = [tex]\displaystyle \frac{77.70 - 56.80}{66-44}[/tex]
m₂ = [tex]\displaystyle \frac{20.9}{22}[/tex]
Because the values of m₁ and m₂ are not the same [tex]\displaystyle \frac{19}{20}[/tex] ≠ [tex]\displaystyle \frac{20.9}{22}[/tex], then x and y have not a proportional relationship.
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