Question

Find the equation of the line passing through $(2,1)$ and parallel to the line $2x-y=4$.

(A) $y=\frac{2}{5}x-1$

(B) $y=5x-2$ (C) $y=2x-3$

(D) None of these

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Answer

The correct answer is (C) $y = 2x - 3$.

Given the line equation $2x - y = 4$, we can rearrange it to the slope-intercept form: $$ y = 2x - 4. $$ Here, the slope $m = 2$. Lines that are parallel share the same slope. Therefore, the slope of the line we are seeking is also $2$.

Assuming the equation of our line is in the form $y = 2x + c$, we need to find $c$ using the given point $(2, 1)$. Substituting the point into the line equation gives: $$ 1 = 2(2) + c. $$ Solving for $c$: $$ 1 = 4 + c \ c = -3. $$

Thus, the equation of the line is: $$ \mathbf{y = 2x - 3}. $$


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