To graph a line with a slope of \(-\frac{1}{8}\) that passes through the point \((-8, 4)\), you can follow these steps:
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Plot the Point: Start by plotting the point \((-8, 4)\) on a Cartesian coordinate system.
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Use the Slope: The slope of \(-\frac{1}{8}\) indicates that for every 8 units you move to the right (positive direction on the x-axis), you move down 1 unit (negative direction on the y-axis). Conversely, for every 8 units you move to the left (negative direction on the x-axis), you move up 1 unit (positive direction on the y-axis).
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Calculate Another Point: From the point \((-8, 4)\), move 8 units to the right (to x = 0) and 1 unit down (to y = 3), giving you the point \((0, 3)\).
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Draw the Line: Now that you have two points, \((-8, 4)\) and \((0, 3)\), you can draw a straight line through them.
Summary of Points
- Point 1: \((-8, 4)\)
- Point 2: \((0, 3)\)
Graphing Process
- Plot both points on the graph.
- Draw a straight line through the two points extending in both directions.
This line represents the equation of the line with the slope of \(-\frac{1}{8}\) passing through the given point.
Equation of the Line
If you prefer, you can also convert this to slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Using point-slope form, the equation of the line can be expressed as: \[ y - 4 = -\frac{1}{8}(x + 8). \] Simplifying this to slope-intercept form will yield the final equation of the line.
Feel free to ask if you need further assistance!