Question

spiral review
for items 1-4, write an equation for the proportional relationship between x and y.
1.
2.
3.
4.

Explanation:

To solve these problems, we use the concept of proportional relationships, which is \( y = kx \), where \( k \) is the constant of proportionality (slope). We'll analyze each graph:

Problem 1

Step 1: Identify two points

Assume the line passes through (1, 3) (estimating from the grid; adjust if needed).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{3}{1} = 3 \)

Step 3: Write the equation

\( y = 3x \)

Problem 2

Step 1: Identify two points

Assume the line passes through (2, 2) (or similar; adjust for grid).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{2}{2} = 1 \)

Step 3: Write the equation

\( y = x \)

Problem 3

Step 1: Identify two points

Assume the line passes through (-3, 6) (since it's in the second quadrant, x negative, y positive).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{6}{-3} = -2 \)

Step 3: Write the equation

\( y = -2x \)

Problem 4

Step 1: Identify two points

Assume the line passes through (-6, 2) (x negative, y positive).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{2}{-6} = -\frac{1}{3} \)

Step 3: Write the equation

\( y = -\frac{1}{3}x \)

Final Answers:

1. \( \boldsymbol{y = 3x} \)
2. \( \boldsymbol{y = x} \)
3. \( \boldsymbol{y = -2x} \)
4. \( \boldsymbol{y = -\frac{1}{3}x} \)

(Note: Answers may vary slightly based on grid interpretation; adjust points for accuracy if needed.)

Answer:

To solve these problems, we use the concept of proportional relationships, which is \( y = kx \), where \( k \) is the constant of proportionality (slope). We'll analyze each graph:

Problem 1

Step 1: Identify two points

Assume the line passes through (1, 3) (estimating from the grid; adjust if needed).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{3}{1} = 3 \)

Step 3: Write the equation

\( y = 3x \)

Problem 2

Step 1: Identify two points

Assume the line passes through (2, 2) (or similar; adjust for grid).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{2}{2} = 1 \)

Step 3: Write the equation

\( y = x \)

Problem 3

Step 1: Identify two points

Assume the line passes through (-3, 6) (since it's in the second quadrant, x negative, y positive).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{6}{-3} = -2 \)

Step 3: Write the equation

\( y = -2x \)

Problem 4

Step 1: Identify two points

Assume the line passes through (-6, 2) (x negative, y positive).

Step 2: Calculate slope \( k \)

\( k = \frac{y}{x} = \frac{2}{-6} = -\frac{1}{3} \)

Step 3: Write the equation

\( y = -\frac{1}{3}x \)

Final Answers:

1. \( \boldsymbol{y = 3x} \)
2. \( \boldsymbol{y = x} \)
3. \( \boldsymbol{y = -2x} \)
4. \( \boldsymbol{y = -\frac{1}{3}x} \)

(Note: Answers may vary slightly based on grid interpretation; adjust points for accuracy if needed.)