Question

instructions: enter your jeopardy gar done, click save & finish. dismiss. undo redo +add row + a constant of 100 if the y is directly proportional to x with a constant of 100 what is the y when x=3 200 if the y is on the proportional to x with a constant to 250 what is the when y = 500 300 if the the constant of proportional is 400 and the x = 1 what is the y 400 if y is directly proportional to x with a constant of 500 what is the y when x = 0.5 500 if the constant of proportionally is 300 and y = 900 what is x

Explanation:

Let's solve the 100 - point question first: "If \( y \) is directly proportional to \( x \) with a constant of 100, what is \( y \) when \( x = 3 \)?"

Step 1: Recall the direct proportion formula

For direct proportion, the formula is \( y=k\times x \), where \( k \) is the constant of proportionality. Here, \( k = 100 \) and \( x = 3 \).

Step 2: Substitute the values into the formula

Substitute \( k = 100 \) and \( x = 3 \) into \( y=k\times x \), we get \( y = 100\times3 \).

Step 3: Calculate the result

\( 100\times3=300 \).

Now the 200 - point question: "If \( y \) is proportional to \( x \) with a constant of 250, what is \( x \) when \( y = 500 \)?" (assuming "constant to 250" is a typo and should be "constant of 250")

Step 1: Recall the direct proportion formula

The formula for direct proportion is \( y = k\times x \), where \( k = 250 \) and \( y = 500 \). We need to solve for \( x \), so we can re - arrange the formula to \( x=\frac{y}{k} \).

Step 2: Substitute the values into the formula

Substitute \( y = 500 \) and \( k = 250 \) into \( x=\frac{y}{k} \), we get \( x=\frac{500}{250} \).

Step 3: Calculate the result

\( \frac{500}{250}=2 \).

300 - point question: "If the constant of proportionality is 400 and \( x = 1 \), what is \( y \)?"

Step 1: Recall the direct proportion formula

The formula for direct proportion is \( y=k\times x \), where \( k = 400 \) and \( x = 1 \).

Step 2: Substitute the values into the formula

Substitute \( k = 400 \) and \( x = 1 \) into \( y = k\times x \), we get \( y=400\times1 \).

Step 3: Calculate the result

\( 400\times1 = 400 \).

400 - point question: "If \( y \) is directly proportional to \( x \) with a constant of 500, what is \( y \) when \( x = 0.5 \)?"

Answer:

s:
100 - point question: \( \boldsymbol{300} \)
200 - point question: \( \boldsymbol{2} \)
300 - point question: \( \boldsymbol{400} \)
400 - point question: \( \boldsymbol{250} \)
500 - point question: \( \boldsymbol{3} \)