Question

find the equation for the line parallel to the given line in passing through the given point.
`y = mx + b`;(x1,y1)

Answer 1

When two lines are parallel they share the same slope, so "m" will be equal across them. We need to find the value "bi", we do that by applying the point to the expression of the line. We have:

`\begin{gathered} y_1=mx_1+b_i \\ b_1=y_1-m_{}x_1 \end{gathered}`

The expression for the new line is:

`\begin{gathered} y=mx+(y_1-mx_1) \\ y-y_1=mx-mx_1 \\ y-y_1=m(x-x_1) \end{gathered}`

The expression of the line is "y-y1=m(x-x1)".