If the line 2x + 3y = 5 and y = mx + c are pa | vedclass

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(C) The given line is $2x + 3y = 5$. Rewriting this in slope-intercept form $y = mx + c$,we get $3y = -2x + 5$,which simplifies to $y = -\frac{2}{3}x

Vedclass · Accepted Answer

$m = -2/3, c = 	ext{any real number}$

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(C) The given line is $2x + 3y = 5$. Rewriting this in slope-intercept form $y = mx + c$,we get $3y = -2x + 5$,which simplifies to $y = -\frac{2}{3}x + \frac{5}{3}$. Comparing this with $y = mx + c$,the slope $m = -\frac{2}{3}$. Two lines are parallel if they have the same slope but different $y$-intercepts (or are identical). Since the question only specifies that the lines are parallel,the slope $m$ must be $-2/3$,while $c$ can be any real number except $5/3$ (if they are distinct parallel lines). However,in the context of general parallel lines,$m = -2/3$ is the necessary condition,and $c$ remains an arbitrary constant.

If the line $2x + 3y = 5$ and $y = mx + c$ are parallel,then:

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