To find the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, we first need to determine the slope of the line using the coordinates you provided, which are \((-3, 4)\) and any other point inferred from the description.
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Identify the Two Points:
- You mentioned a point on the line \((-3, 4)\).
- Since the line goes downwards, we can determine another point from the description, for example, using the chosen endpoints in your description.
If we consider the endpoints for the x-axis, we might take \((-5, -1)\) as one point.
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Calculate the Slope (\(m\)): The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Let's take the points \((-3, 4)\) and \((-5, -1)\):
- \((x_1, y_1) = (-3, 4)\)
- \((x_2, y_2) = (-5, -1)\) \[ m = \frac{-1 - 4}{-5 - (-3)} = \frac{-5}{-5 + 3} = \frac{-5}{-2} = \frac{5}{2} \]
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Find the Y-Intercept (\(b\)): We can now use the slope and one of the points to find the y-intercept. Let's use the point \((-3, 4)\): Plugging into the slope-intercept equation: \[ y = mx + b \] Substituting \(m\) and the point values: \[ 4 = \frac{5}{2}(-3) + b \] \[ 4 = -\frac{15}{2} + b \] To find \(b\): \[ b = 4 + \frac{15}{2} = \frac{8}{2} + \frac{15}{2} = \frac{23}{2} \]
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Write the Final Equation: Now substituting back into the slope-intercept form: \[ y = \frac{5}{2}x + \frac{23}{2} \]
So the equation of the line in slope-intercept form is:
Answer: \(y = \frac{5}{2}x + \frac{23}{2}\)