To find the equations of the lines represented by the points provided, we will first determine the slopes (m) and intercepts (b) for each line formed by the specified points. The general equation of a line is represented as \(y = mx + b\).
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Line J: Points \(a = (0, 8)\) and \(b = (3, 0)\)
- Find the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{3 - 0} = \frac{-8}{3} \]
- Use the point-slope form with point \(b\) (3, 0): \[ y - 0 = \frac{-8}{3}(x - 3) \] Simplifying gives: \[ y = \frac{-8}{3}x + 8 \]
- Therefore, Line J’s equation is: \[ \boxed{y = \frac{-8}{3}x + 8} \]
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Line K: Points \(b = (3, 0)\) and \(c = (-7, 0)\)
- Since both points have the same y-coordinate (0), this is a horizontal line:
- The equation is: \[ y = 0 \]
- Therefore, Line K’s equation is: \[ \boxed{y = 0} \]
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Line L: Points \(c = (-7, 0)\) and \(e = (-5, -5)\)
- Find the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 0}{-5 - (-7)} = \frac{-5}{2} \]
- Use the point-slope form with point \(c\) (-7, 0): \[ y - 0 = \frac{-5}{2}(x + 7) \] Simplifying gives: \[ y = \frac{-5}{2}x - \frac{35}{2} \]
- Therefore, Line L’s equation is: \[ \boxed{y = \frac{-5}{2}x - \frac{35}{2}} \]
In summary, the equations are:
- Line J: \(y = \frac{-8}{3}x + 8\)
- Line K: \(y = 0\)
- Line L: \(y = \frac{-5}{2}x - \frac{35}{2}\)