Question

Which one of these relationships is different than the other three? Explain how you know. Hint: Find all

Answer 1

Answer:

Graph 2 has a different constant of proportionality

Step-by-step explanation:

See attachment for graphs

To calculate the constant of proportionality, we simply determine the slope of each graph using

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where x's and y's are corresponding values of x and y

Graph 1:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (0.8,4)$

Substitute these values in: $m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - 0}{0.8 - 0}$

$m = \frac{4}{0.8}$

$m = 5$

Graph 2:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (10,55)$

Substitute these values in: $m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{55 - 0}{10 - 0}$

$m = \frac{55}{10}$

$m = 5.5$

Graph 3:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (4,20)$

Substitute these values in: $m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{20 - 0}{4 - 0}$

$m = \frac{20}{4}$

$m = 5$

Graph 4:

$(x_1,y_1) = (0,0)$

$(x_2,y_2) = (10,50)$

Substitute these values in: $m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{50 - 0}{10 - 0}$

$m = \frac{50}{10}$

$m = 5$

From the calculations above, graph 2 has a different constant of proportionality of 5.5 while others have 5 as their constant of proportionality