Question

The equation of the line which is parallel to \(x+\frac{1}{2}y=\frac{3}{2}\) and passing through (1,3) is

• A. 2x+y=7
• B. 2x+y+5=0
• C. 2x+y=3
• D. 2x+y=6
• E. 2x+y=5

Answer 1

Answer: (E)

Step 1: Convert the given equation to slope-intercept form 

Given equation: \( x + \frac{1}{2}y = \frac{3}{2} \)

Rearrange for \( y \):

\(\frac{1}{2}y = -x + \frac{3}{2}\)

Multiply by 2 to clear the fraction:

\( y = -2x + 3 \)

Step 2: Identify the slope

The slope of the given line is \( m = -2 \).

Step 3: Use point-slope form for the new line

The required line is parallel, so it has the same slope \( m = -2 \) and passes through (1,3).

Using point-slope form:

\( y - y_1 = m(x - x_1) \)

\( y - 3 = -2(x - 1) \)

Expanding:

\( y - 3 = -2x + 2 \)

\( y = -2x + 5 \)

Step 4: Convert to standard form

\( 2x + y = 5 \)

Thus, the correct answer is:

\( 2x + y = 5 \)