Question

Is this the correct graph of y=−13x+4 ?(1 point) 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 has a positive slope. No, it is not the correct graph because this graph has a positive slope. 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 used (0,3) as the y -intercept.

Answer 1

To determine if a given graph represents the equation \( y = -13x + 4 \), we need to analyze its slope and y-intercept.

1. The slope (m) of the equation is -13, which indicates that the graph will be a downward sloping line.
2. The y-intercept (b) is 4, which means the graph will cross the y-axis at the point (0, 4).

Based on this information, we can evaluate the responses:

- “Yes, it is the correct graph because this graph has a y-intercept of (0, 3)”: This is incorrect; the y-intercept is (0, 4).
- “Yes, it is the correct graph because this graph has a y-intercept of left parenthesis 0 comma 3 right parenthesis”: This is incorrect for the same reason.
- “No, it is not the correct graph because this graph has a positive slope”: This is incorrect; the slope is negative (-13).
- “No, it is not the correct graph because this graph has a positive slope”: This is also incorrect for the same reason.
- “Yes, it is the correct graph because this graph has a y-intercept of (0, 4)”: This is correct if the graph really does have this y-intercept and the correct slope.
- “Yes, it is the correct graph because this graph has a y-intercept of left parenthesis 0 comma 4 right parenthesis”: This is also correct if the graph has the correct characteristics.

If the graph has a y-intercept at (0, 4) and a negative slope, then the last two responses would be correct. If the graph does not match these characteristics, then it would not be correct.