To determine if the provided graph is correct, we can analyze the two points given: (1, -7) and (0, 10).
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Identify the y-intercept: The y-intercept is the point where the graph crosses the y-axis. From the point (0, 10), we can see that the y-intercept is 10.
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Calculate the slope (m): The slope of a line can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (1, -7) and (0, 10):
- Let (x1, y1) = (0, 10) and (x2, y2) = (1, -7)
\[ m = \frac{-7 - 10}{1 - 0} = \frac{-17}{1} = -17 \]
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Determine the linear equation: With the slope and the y-intercept, we can write the equation of the line in slope-intercept form (y = mx + b). The equation based on our calculations is:
\[ y = -17x + 10 \]
Now, from your question options regarding the slope and y-intercept of a line called "3zy 107" (which I assume is a typo or error), we can analyze the following statements provided:
- "No, it is not the correct graph because the slope is 3 and the y-intercept is (0,10)."
- "Yes, it is the correct graph because the slope is 3 and the y-intercept is (0,10)."
- "No, it is not the correct graph because the slope is -3 and the y-intercept is (0,10)."
- "Yes, it is the correct graph because the slope is -3 and the y-intercept is (0,10)."
Based on our findings, the slope is neither 3 nor -3 – it is actually -17 with the y-intercept being (0, 10). Therefore, none of the given options accurately describe the situation.
So the correct conclusion is: No, it is not the correct graph because the slope is -17 and the y-intercept is (0,10). However, this option is not provided in your list. If you had a choice reflecting the calculator result precisely, that would be the accurate answer.