Question

Which graph represents the equation y=1/3x−4?

A. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair negative 2 comma 1 end ordered pair.

B. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair 0 comma negative 4 end ordered pair and begin ordered pair 3 comma negative 3 end ordered pair.

C. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair negative 4 comma 0 end ordered pair and begin ordered pair negative 3 comma 3 end ordered pair.

D. Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through begin ordered pair negative 4 comma 0 end ordered pair and begin ordered pair 3 comma negative 3 end ordered pair.

Answer 1

To determine which graph represents the equation \( y = \frac{1}{3}x - 4 \), we can look for key characteristics of the line defined by this equation.

1. **Y-Intercept**: The equation \( y = \frac{1}{3}x - 4 \) indicates that the y-intercept (where \( x = 0 \)) is \( -4 \). Thus, one point on the line is \( (0, -4) \).

2. **Slope**: The slope \( \frac{1}{3} \) means for every increase of 3 units in \( x \), \( y \) increases by 1 unit. We can find another point on the line by starting at the y-intercept and moving according to the slope:
- Start at \( (0, -4) \).
- Increase \( x \) by 3: \( (3, -4 + 1) = (3, -3) \) (which means for \( x = 3 \), \( y = -3 \)).

Thus, we have two points on the line: \( (0, -4) \) and \( (3, -3) \).

Now, we can analyze the answer choices:

- **A**: Points \( (0, -4) \) and \( (-2, 1) \) — Does not match our points.
- **B**: Points \( (0, -4) \) and \( (3, -3) \) — Matches our points!
- **C**: Points \( (-4, 0) \) and \( (-3, 3) \) — Does not match our points.
- **D**: Points \( (-4, 0) \) and \( (3, -3) \) — Does not match the y-intercept.

**Conclusion**: The correct graph that represents the equation \( y = \frac{1}{3}x - 4 \) is **B**.