Question

PLEASES HELPPP !!!!

Which of the following is an equation of a line parallel to the equation y=1/2x+1?
a. y=-1/2x+1
b. y=-2x-5
c. y=1/2x-5
d. y=2x-5

Answer 1

`\large\boxed{C.\ y=(1)/(2)x-5}`

Explanation:

The slope-intercept form of an equation of a line:

`y=mx+b`

m - slope

b - y-intercept

`\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff\ m_1m_2=-1\to m_2=(1)/(m_1)\\\\l\ \parallel\ k\iff m_1=m_2`

Parallel line have the same slope.

Therefore a line parallel to the line
`y=(1)/(2)x+1` has equation

`y=(1)/(2)x+b`