Question

1. circle all of the equations that are parallel to the line ( y=\frac{1}{2}x ). (2 pts)

a. ( y=\frac{1}{2}x + 9 ) b. ( y+\frac{1}{2}x = 0 )
c. ( 2y - x = 4 ) d. ( \frac{1}{2}y = x )

Explanation:

Step1: Recall the slope - intercept form

The equation of a line is \(y = mx + b\), where \(m\) is the slope. For two lines to be parallel, their slopes \(m\) must be equal. The given line is \(y=\frac{1}{2}x\), so its slope \(m = \frac{1}{2}\).

Step2: Analyze each option

• Option A:

The equation \(y=\frac{1}{2}x + 9\) is in slope - intercept form \(y=mx + b\). Here, \(m=\frac{1}{2}\).

• Option B:

Rewrite \(y+\frac{1}{2}x = 0\) as \(y=-\frac{1}{2}x+0\). The slope \(m =-\frac{1}{2}\).

• Option C:

Rewrite \(2y−x = 4\) as \(2y=x + 4\), then \(y=\frac{1}{2}x+2\). The slope \(m=\frac{1}{2}\).

• Option D:

Rewrite \(\frac{1}{2}y=x\) as \(y = 2x\). The slope \(m = 2\).

Answer:

A. \(y=\frac{1}{2}x + 9\), C. \(2y−x = 4\)