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

Question

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.