Question

Which is an equation of the line parallel to y = 2x + 7 and passes through (-1, 3)?

Answer 1

The equation of line parallel to y = 2x + 7 and passes through (-1, 3) is:
`y = 2x+5`

Explanation:

Given equation of line is:

y = 2x + 7

The general form of equation in slope-intercept form is:

`y=mx+b`

Here m is the slope and b is the y-intercept

Comparing the equations, we get

m = 2

Let m_1 be the slope of line parallel to given line

`m_1 = m\\m_1 = 2`

The equation of line parallel to given line will be:

`y=m_1x+b`

Putting the value of slope

`y = 2x+b`

To find the y-intercept, putting (-1,3) in the equation

`3 = 2(-1)+b\\3 = -2+b\\3+2 = b\\b = 5`

The equation is:

`y = 2x+5`

Hence,

The equation of line parallel to y = 2x + 7 and passes through (-1, 3) is:
`y = 2x+5`