To write the equations of lines J, K, and L in the slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \) from the given coordinates.
Line J:
Points: A(0, 8) and B(3, 0)
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Find the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{3 - 0} = \frac{-8}{3} \]
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Find the y-intercept \( b \): Using point A(0, 8), since the y-intercept occurs when \( x = 0 \): \[ b = 8 \]
So the equation of Line J is: \[ y = -\frac{8}{3}x + 8 \]
Line K:
Points: E(-5, -5) and F(0, -3)
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Find the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-5)}{0 - (-5)} = \frac{-3 + 5}{0 + 5} = \frac{2}{5} \]
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Find the y-intercept \( b \): Using point F(0, -3): \[ b = -3 \]
So, the equation of Line K is: \[ y = \frac{2}{5}x - 3 \]
Line L:
Points: C(-7, 0) and D(0, 3)
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Find the slope \( m \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{0 - (-7)} = \frac{3}{7} \]
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Find the y-intercept \( b \): Using point D(0, 3): \[ b = 3 \]
So, the equation of Line L is: \[ y = \frac{3}{7}x + 3 \]
Summary:
- Line J: \( y = -\frac{8}{3}x + 8 \)
- Line K: \( y = \frac{2}{5}x - 3 \)
- Line L: \( y = \frac{3}{7}x + 3 \)