To determine if the graph is correct for the equation \(y = -13x + 4\), we need to analyze the information given:
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Find the y-intercept: The y-intercept of a linear equation in slope-intercept form \(y = mx + b\) is given by the value of \(b\). In this case, the y-intercept is \(4\), which corresponds to the point \((0, 4)\).
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Consider the slope: The slope of the line is \(-13\), which is a negative number. This means the line will be decreasing as we move from left to right. The two points on the graph are \((0, 3)\) and \((3, 2)\). The slope between these points is \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3}, \] which is a positive slope.
Now, looking at the responses:
- The graph cannot be correct since the y-intercept is at \((0, 4)\) and the graph shows \((0, 3)\).
- The slope from the points \((0, 3)\) and \((3, 2)\) is a positive slope, while the equation describes a line with a negative slope.
Based on these analyses, the correct answer is: No, it is not the correct graph because this graph has a positive slope.
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