Is this the correct graph of y=−1/3x+4 ?(1 point) graph points are 0,3 and 3,2

Question

Responses Yes, it is the correct graph because this graph has a y -intercept of (0,3) . Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis . No, it is not the correct graph because this graph used (0,3) as the y -intercept. No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept. Yes, it is the correct graph because this graph has a y -intercept of (0,4) . Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis . No, it is not the correct graph because this graph has a positive slope. No, it is not the correct graph because this graph has a positive slope.

Answer 1

To determine if the graph correctly represents the equation \(y = -\frac{1}{3}x + 4\), we need to analyze the y-intercept and the slope of the line.

1. Y-intercept: The y-intercept of a line in the slope-intercept form \(y = mx + b\) is \(b\). In this case, \(b = 4\), which means the y-intercept is at \((0, 4)\).

2. Slope: The slope \(m\) is \(-\frac{1}{3}\), which is negative, indicating that the line will fall as \(x\) increases.

Given the points mentioned in the question:

• \((0, 3)\) and \((3, 2)\)

The graph provided would have a y-intercept at \((0, 3)\), which is not correct according to the equation (the correct y-intercept is \((0, 4)\)). Additionally, the presence of positive points does not reflect the negative slope described by the equation.

Conclusion:

No, it is not the correct graph because this graph used (0, 3) as the y-intercept.