Question

GP Guided Practice 1 Given the line y=(1/2)x+1, which of the following is NOT parallel to the line?

A) y=(1/2)x-3
B) x-2y=3
C) y-2=(1/2)(x-2)
D) 2x-y=3

Answer 1

To determine which equation is not parallel to the given line, we need to compare their slopes. The equation y=(1/2)x+1 has a slope of 1/2. By comparing the slopes of the given equations, we find that D) 2x-y=3 is not parallel to the given line.

Step-by-step explanation:

To determine which equation is not parallel to the line y=(1/2)x+1, we need to compare the slopes of the given equations to the slope of the given line. The slope of the equation y=(1/2)x+1 is 1/2.

• A) y=(1/2)x-3: This equation has the same slope of 1/2 as the given line, so it is parallel.
• B) x-2y=3: Rearranging the equation in slope-intercept form, we get y=(1/2)x-3/2. This equation has the same slope of 1/2 as the given line, so it is parallel.
• C) y-2=(1/2)(x-2): Simplifying the equation, we get y=(1/2)x-1. This equation has the same slope of 1/2 as the given line, so it is parallel.
• D) 2x-y=3: Rearranging the equation in slope-intercept form, we get y=2x-3. This equation has a slope of 2, which is not the same as the slope of 1/2 for the given line. Therefore, D) 2x-y=3 is the equation that is not parallel to the given line.