To graph the line with a slope of \( \frac{3}{4} \) that passes through the point \((-3, -5)\), follow these steps:
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Identify the slope and point: The slope \( m = \frac{3}{4} \) and the point is \( (-3, -5) \).
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Use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Here, \( (x_1, y_1) = (-3, -5) \) and \( m = \frac{3}{4} \).
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Substitute the values into the equation: \[ y - (-5) = \frac{3}{4}(x - (-3)) \] \[ y + 5 = \frac{3}{4}(x + 3) \]
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Simplify the equation: \[ y + 5 = \frac{3}{4}x + \frac{3}{4} \cdot 3 \] \[ y + 5 = \frac{3}{4}x + \frac{9}{4} \] \[ y = \frac{3}{4}x + \frac{9}{4} - 5 \] To subtract 5, convert 5 into quarters: \[ y = \frac{3}{4}x + \frac{9}{4} - \frac{20}{4} \] \[ y = \frac{3}{4}x - \frac{11}{4} \]
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Graphing the line:
- Start at the point \((-3, -5)\).
- From this point, use the slope \( \frac{3}{4} \) to find another point. This means for every 4 units you move to the right (positive direction), you will move up 3 units.
- Move from \((-3, -5)\) to the right 4 units to \((1, -5)\) and then up 3 units to \((1, -2)\). This gives you another point \((1, -2)\).
- Connect the points \((-3, -5)\) and \((1, -2)\) to draw the line.
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Final Line Equation: The equation of the line is \( y = \frac{3}{4}x - \frac{11}{4} \).
By following these steps, you can accurately graph the line on a coordinate plane.