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Math Question

In this coordinate plane, line \( m \) is parallel to line \( n \). Complete the proof that the slope of line \( m \) is equal to the slope of line \( n \). Since the \( y \)-axis is a transversal of parallel lines \( m \) and \( n \), altemate interior angles - are congruent. Also, \( \angle A C B \) and \( \angle D C E \) are the - Since corresponding sides of similar triangles are proportional, - Further, since \( A C=a, B C=b, D C=d \), and \( E C=e \), - by substitution. The slope of a line is defined as the change in \( y \) divided by the change in \( x \). Two points on line \( m \) are \( A(a, 0) \) and \( B(0, b) . \) So, the slope of line \( m \) is - Two points on line \( n \) are \( D \) \( (-d, 0) \) and \( E(0,-e) . \) So, the slope of line \( n \) is - Therefore, the slope of line \( m \) is equal to the slope of line \( n \).

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