To write the equations of the lines \(J\), \(K\), and \(L\) in the form \(y = mx + b\), we need to find the slope (\(m\)) and the y-intercept (\(b\)) for each line given the points provided for each line.
Line J
Points on line J: \(a(0, 8)\) and \(b(3, 0)\).
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Find the slope (m): The formula for slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points \(a(0, 8)\) and \(b(3, 0)\): \[ m = \frac{0 - 8}{3 - 0} = \frac{-8}{3} = -\frac{8}{3} \]
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Find the y-intercept (b): Since the y-intercept is the value of \(y\) when \(x=0\), we can directly see from point \(a(0, 8)\) that: \[ b = 8 \]
Thus, the equation of line \(J\) is: \[ y = -\frac{8}{3}x + 8 \]
Line K
The information provided for line K is not complete. If you have specific points for line K, please share them.
Line L
Points on line L: \(c(-7, 0)\) and \(D(0, 3)\).
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Find the slope (m): Using the same formula for slope, Substituting the points \(c(-7, 0)\) and \(D(0, 3)\): \[ m = \frac{3 - 0}{0 - (-7)} = \frac{3}{7} \]
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Find the y-intercept (b): Again, since we have point \(D(0, 3)\): \[ b = 3 \]
Thus, the equation of line \(L\) is: \[ y = \frac{3}{7}x + 3 \]
Summary
- Line J: \(y = -\frac{8}{3}x + 8\)
- Line K: Needs specific points to determine the equation.
- Line L: \(y = \frac{3}{7}x + 3\)
Please provide additional information for line K so I can assist you further!