The equation you've provided is a linear equation in two variables, \(x\) and \(y\). It can be rewritten or analyzed in various forms depending on what you need. Here are a few ways to work with it:
- Slope-Intercept Form: To express the equation in the slope-intercept form \(y = mx + b\), solve for \(y\):
\[ y = -8x - 17 \]
This indicates that the slope (\(m\)) is -8 and the y-intercept (\(b\)) is -17.
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Standard Form: Your equation is already in standard form \(Ax + By = C\), where \(A = 8\), \(B = 1\), and \(C = -17\).
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Graphing: To graph the line represented by this equation, you can find two points. For example:
- Let \(x = 0\): \[ y = -8(0) - 17 = -17 \quad \Rightarrow \quad (0, -17) \]
- Let \(x = 1\): \[ y = -8(1) - 17 = -25 \quad \Rightarrow \quad (1, -25) \] You can then plot these points on a coordinate plane and draw the line through them.
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Finding Intercepts:
- y-intercept: Set \(x = 0\): \[ y = -17 \quad \Rightarrow \quad (0, -17) \]
- x-intercept: Set \(y = 0\): \[ 0 = -8x - 17 \quad \Rightarrow \quad 8x = -17 \quad \Rightarrow \quad x = -\frac{17}{8} = -2.125 \quad \Rightarrow \quad \left(-\frac{17}{8}, 0\right) \]
If you need further analysis or a specific type of solution related to this equation, please let me know!