Question

The graphs show the amount of sugar in two kinds of juice.

Answer 1

Answer:

Pat a) The unit rate of graph at left is $25\ \frac{grams}{cup}$

Part b) The unit rate of graph at right is $40\ \frac{grams}{cup}$

see the attached figure

Step-by-step explanation:

we know that

The unit rate of a linear equation is the same that the slope of the linear equation

step 1

Find the slope of the graph at left

This graph represent a proportional relationship (because the line passes through the origin)

The slope is equal to the constant of proportionality k

$k=\frac{y}{x}$

we have the point (1,25)

substitute the values in the formula

$k=\frac{25}{1}=25\ \frac{grams}{cup}$

step 2

Find the slope of the graph at right

we have the points (2,80) and (3,120)

This graph represent a proportional relationship (because the line passes through the origin)

The slope is equal to the constant of proportionality k

$k=\frac{y}{x}$

Is necessary only one point to determine the constant of proportionality

take the point (2,80)

substitute the values

$k=\frac{80}{2}=40\ \frac{grams}{cup}$

Verify

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points (2,80) and (3,120)

substitute the values

$m=\frac{120-80}{3-2}$

$m=\frac{140}{1}=40\ \frac{grams}{cup}$