Use the image to answer the question.

Question

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−1/3x+4 ?

Answer 1

To determine if the line connecting the points (0, 3) and (3, 2) represents the equation \( y = -\frac{1}{3}x + 4 \), we can check if both plotted points satisfy the equation.

1. Check point (0, 3): \[ y = -\frac{1}{3}(0) + 4 = 0 + 4 = 4 \] The y-coordinate at x = 0 is 4; the point (0, 3) does not satisfy the equation.

2. Check point (3, 2): \[ y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3 \] The y-coordinate at x = 3 is 3; the point (3, 2) does not satisfy the equation.

Since neither point lies on the line described by the equation \( y = -\frac{1}{3}x + 4 \), this is not the correct graph for that equation. The line connecting those points does not represent the equation.