To find the equation of a line in slope-intercept form (which is \( y = mx + b \)), we need to determine two things: the slope \( m \) and the y-intercept \( b \).
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Identify two points on the line: From your description, it seems that you have the graph along with points on both axes. Without exact coordinates, let's assume you want to calculate the slope using some hypothetical points.
For example, if you have two points, for instance, point A at \( (-5, 6) \) and point B at \( (1, 1) \) (you can adjust this based on the actual graph you have):
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Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 6}{1 - (-5)} = \frac{-5}{1 + 5} = \frac{-5}{6} \]
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Find the y-intercept (b): Use one of the points to find the y-intercept. Let's use point A \((-5, 6)\): \[ y = mx + b \implies 6 = \left(-\frac{5}{6}\right)(-5) + b \] \[ 6 = \frac{25}{6} + b \] \[ b = 6 - \frac{25}{6} = \frac{36}{6} - \frac{25}{6} = \frac{11}{6} \]
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Write the equation in slope-intercept form: Now we can express the equation of the line: \[ y = -\frac{5}{6}x + \frac{11}{6} \]
So you can fill in the values:
- Slope (m): \(-\frac{5}{6}\)
- Y-intercept (b): \(\frac{11}{6}\)
Therefore, the equation of the line in slope-intercept form is:
\[ y = -\frac{5}{6}x + \frac{11}{6} \]
Make sure to adjust the points based on your graph for the correct slope and intercept if my assumptions about your points were incorrect!