# Find the equation of the line passing through (2,1) and parallel to the line 2x-y=4. (A) y=(2/5)x-1 (B) y=5x-2 (C) y=2x-3 (D) None of these

## 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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