Question

Two lines are parallel. The equation of the first line is y = 2x + 3. Which of these could be the equation of the other line?A. y = 2xB. y = -1/2x C. y = 1/2xD. y = 2x

Answer 1

The equation that could be the equation of the other line is;

`y=2x`

Step-by-step explanation:

Given that;

Two lines are parallel.

And the equation of the first line is;

`y=2x+3`

Recall that, for two lines to be parallel they must have equal slope;

`m_1=m_2`

For the first line, the slope m is;

`m_1=2`

Since they are parallel, then the slope of the second line must also be equal to;

`\begin{gathered} m_1=m_2=2 \\ m_2=2 \end{gathered}`

Writing the equation of the second line we have;

`\begin{gathered} y=m_2x+b \\ y=2x+b \end{gathered}`

At b = 0, then;

`y=2x`

The equation that could be the equation of the other line is;

`y=2x`