7 of 187 of 18 Items

Question

Question
The amount of money that Sarah earns varies directly with the number of hours worked. If Sarah earns $320 for working 40 hours, determine the constant of proportionality.(1 point)
$
per hour (Remember to include the hundredths place, two digits after the decimal.)
Skip to navigation

page 1 of 1
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the constant of proportionality for Sarah's earnings, you can use the relationship that the amount earned (\(E\)) is directly proportional to the number of hours worked (\(H\)). This can be expressed with the formula:

\[ E = k \cdot H \]

where \(k\) is the constant of proportionality (the rate of pay per hour).

From the information given:

• Sarah earns \(E = 320\) dollars
• She works \(H = 40\) hours

Now, we can substitute these values into the formula and solve for \(k\):

\[ 320 = k \cdot 40 \]

To find \(k\), divide both sides by 40:

\[ k = \frac{320}{40} \]

Calculating this gives:

\[ k = 8 \]

So the constant of proportionality, which represents Sarah's earnings per hour, is:

\[ k = 8.00 \]

Thus, the answer is:

$8.00 per hour.

Answer 2

9 of 189 of 18 Items

Question
Select THREE characteristics of proportional relationships on a graph.(1 point)
Responses

The ratio of yx
is the same for all points on the line.
The ratio of y over x is the same for all points on the line.

The x values are always larger than the y values.
The x values are always larger than the y values.

The y values are always larger than the x values.
The y values are always larger than the x values.

It passes through the origin (0, 0).
It passes through the origin (0, 0).

The points will form a straight line.
The points will form a straight line.
Skip to navigation

page 1 of 1
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 3

In a proportional relationship represented on a graph, the following three characteristics are true:

1. The ratio of \(y\) over \(x\) is the same for all points on the line.
   This means that for any point \((x, y)\) on the line, the ratio \(\frac{y}{x}\) is constant.

2. It passes through the origin (0, 0).
   This means that when both \(x\) and \(y\) are zero, the line representing the proportional relationship starts from the origin.

3. The points will form a straight line.
   In a proportional relationship, the points form a straight line indicating a constant rate of change.

Thus, the three correct characteristics of proportional relationships on a graph are:

• The ratio of \(y\) over \(x\) is the same for all points on the line.
• It passes through the origin (0, 0).
• The points will form a straight line.