Question

12 of 13 1 write equations for proportional relationships from tables and graphs
question
while relaxing on his front porch, ruben notices a garden snail crawling on the sidewalk.
ruben is amazed at how slowly the snail moves, so he starts timing it.

there is a proportional relationship between the amount of time (in minutes) that ruben
spends timing the snail, x, and the distance (in feet) that the snail moves, y.

x (minutes)	y (feet)
19	38
23	46
28	56

write an equation for the relationship between x and y. simplify any fractions.

y =

Explanation:

Step1: Recall proportional relationship formula

For a proportional relationship, the formula is \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Calculate \( k \) using a data point

Take the first data point \( x = 7 \), \( y = 14 \). Substitute into \( y = kx \): \( 14 = k \times 7 \). Solve for \( k \): \( k=\frac{14}{7}=2 \).

Step3: Verify \( k \) with other points

Check second point: \( x = 19 \), \( y = 38 \). \( k=\frac{38}{19}=2 \). Third point: \( x = 23 \), \( y = 46 \). \( k=\frac{46}{23}=2 \). Fourth point: \( x = 28 \), \( y = 56 \). \( k=\frac{56}{28}=2 \). So \( k = 2 \) is consistent.

Step4: Write the equation

Substitute \( k = 2 \) into \( y = kx \), we get \( y = 2x \).

Answer:

\( y = 2x \)