Question

What is the equation of the line parallel to the line $y=3x+2$ passing through the point $(10,1)$ $?$

Answer 1

Find the equation of the line parallel to the line $y=3x+2$ passing through the point $(10,1)$:

The slope-intercept form is $\mathit{y}\mathbf{=}\mathit{m}\mathit{x}\mathbf{+}\mathit{c}$, where $m$ is the slope and $b$ is the $y-intercept$:

Using the slope-intercept form, the slope of the given line is $3$.

Since the slope of parallel line must be equal, the slope of line parallel to the given line is $3$.

Let $(x_1,y_1)=(10,1)$

Now, use the point-slope formula to find the equation of the line parallel to the given line:

$\mathit{y}\mathbf{-}{\mathit{y}}_{\mathbf{1}}\mathbf{=}\mathit{m}\mathbf{(}\mathit{x}\mathbf{-}{\mathit{x}}_{\mathbf{1}}\mathbf{)}$

Substitute $3$ for m and $(10,1)$ for $(x_1,y_1)$ in the point-slope formula:

$\begin{array}{rcl}y-1& =& 3(x-10)\\ & \Rightarrow & y-1=3x-30\\ & \Rightarrow & y=3x-29\end{array}$

Hence, the equation of the line parallel to the line $y=3x+2$ passing through the point $(10,1)$ is $\mathit{y}\mathbf{=}\mathbf{3}\mathit{x}\mathbf{-}\mathbf{29}\mathbf{.}$