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
?(1 point)

Answer 1

To determine if the line represented on the graph is the correct graph of the equation \( y = -\frac{1}{3}x + 4 \), we can check the two given points against the equation.

1. Point (0, 3):

   • Substitute \( x = 0 \) into the equation: \[ y = -\frac{1}{3}(0) + 4 = 4 \] This does not equal 3, so point (0, 3) is not on the line.

2. Point (3, 2):

   • Substitute \( x = 3 \) into the equation: \[ y = -\frac{1}{3}(3) + 4 = -1 + 4 = 3 \] This does not equal 2, so point (3, 2) is also not on the line.

Since neither point (0, 3) nor point (3, 2) lies on the line described by the equation \( y = -\frac{1}{3}x + 4 \), we can conclude that this is not the correct graph of the equation.