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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=−13x+4
?(1 point)
Responses

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 .

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 has a positive slope.

1 answer

To determine whether the graph corresponds to the equation \( y = -13x + 4 \):

  1. Identify the y-intercept: The y-intercept from the equation \( y = -13x + 4 \) is \( (0, 4) \). This means when \( x = 0 \), \( y = 4 \).

  2. Check the plotted points:

    • The plotted points given are \( (0, 3) \) and \( (3, 2) \).
    • The point \( (0, 3) \) indicates that the graph intersects the y-axis at 3, not 4.

  3. Determine the slope: The slope \( m \) of the line given by the equation is \(-13\), which is negative. Since the graph with points \( (0, 3) \) and \( (3, 2) \) shows a downward trend, this part is consistent with a negative slope.

Given the findings:

  • The y-intercept of the provided points is incorrect as it shows \( (0, 3) \) instead of \( (0, 4) \).
  • The graph does show a negative slope.

Given all this information, the best response would be:

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