The equation of a line which is parallel to t | vedclass

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Question

(C) Two lines are parallel if their slopes are equal. The given line is $x+3y=5$,which can be written in the slope-intercept form $y = mx + c$ as $3y

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$x+3y=10$

Vedclass · Answer

(C) Two lines are parallel if their slopes are equal. The given line is $x+3y=5$,which can be written in the slope-intercept form $y = mx + c$ as $3y = -x + 5$,or $y = -\frac{1}{3}x + \frac{5}{3}$. The slope of this line is $m = -\frac{1}{3}$. $A$ line parallel to this will have the same slope $m = -\frac{1}{3}$ and will be of the form $x+3y=k$ for some constant $k$. Comparing the given options,the equation $x+3y=10$ has the same coefficients for $x$ and $y$ as the original line,meaning it has the same slope. Therefore,$x+3y=10$ is parallel to $x+3y=5$.

The equation of a line which is parallel to the line $x+3y=5$ is $\ldots \ldots \ldots \ldots$

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