To write the equation of a line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can follow these steps:
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Identify the slope and a point on the line:
The slope \( m = -\frac{3}{4} \) and we have the point \( (16, -18) \). -
Use the point-slope form of the line equation:
The point-slope form is given by \( y - y_1 = m(x - x_1) \). Here, \( (x_1, y_1) = (16, -18) \): \[ y - (-18) = -\frac{3}{4}(x - 16) \] This simplifies to: \[ y + 18 = -\frac{3}{4}(x - 16) \] -
Distribute the slope on the right-hand side: \[ y + 18 = -\frac{3}{4}x + \frac{3}{4} \times 16 \] Calculate \( \frac{3}{4} \times 16 = 12 \): \[ y + 18 = -\frac{3}{4}x + 12 \]
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Isolate \( y \) by subtracting 18 from both sides: \[ y = -\frac{3}{4}x + 12 - 18 \] Simplify \( 12 - 18 = -6 \): \[ y = -\frac{3}{4}x - 6 \]
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Final equation:
The equation of the line in slope-intercept form is: \[ y = -\frac{3}{4}x - 6 \]
This is the required equation of the line.