Question

m/j accel math gr 7 - zielske (lms)
4 - 1: lesson quiz (lms graded)
is there a proportional relationship between x and y? explain.

no; all ratios \\( \frac { y } { x } \\) are not equivalent.

yes; each x value and y value increases by 2.

yes; the difference between each x value and y value is 3.

no; all ratios \\( \frac { x } { y } \\) are greater than 1.

Explanation:

Step1: Calculate the ratio of \(y\) to \(x\) for each pair

For \(x = 8,y = 5\), the ratio is \(\frac{y}{x}=\frac{5}{8}=0.625\).
For \(x = 10,y = 7\), the ratio is \(\frac{y}{x}=\frac{7}{10}=0.7\).
For \(x = 12,y = 9\), the ratio is \(\frac{y}{x}=\frac{9}{12}=\frac{3}{4}=0.75\).
For \(x = 14,y = 11\), the ratio is \(\frac{y}{x}=\frac{11}{14}\approx0.786\).

Step2: Check for proportionality

In a proportional relationship, the ratio \(\frac{y}{x}\) (constant of proportionality \(k\)) should be the same for all pairs of \(x\) and \(y\) values. Since \(0.625
eq0.7
eq0.75
eq0.786\), the ratios \(\frac{y}{x}\) are not equivalent.

Answer:

No; all ratios \(\frac{y}{x}\) are not equivalent.