# How do you write an equation of a line going through (d, 0) parallel to y = mx + c?

Jan 25, 2017

$y = \textcolor{b l u e}{m} \left(x - \textcolor{red}{d}\right)$

Or

$y = m x - m d$

#### Explanation:

The point-slope formula can be used to find the equation being asked for in the equation.

First, determine the slope. Because the problem is asking for a parallel line it will have the same slope as the line given in the problem. And because the line given in the problem is in slope-intercept form we can extract the slope directly from the given equation.

The slope-intercept form of a linear equation is:

$y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

Therefore the slope we will use to answer this question is $\textcolor{red}{m}$

The point-slope formula states: $\left(y - \textcolor{red}{{y}_{1}}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{{x}_{1}}\right)$

Where $\textcolor{b l u e}{m}$ is the slope and $\textcolor{red}{\left(\left({x}_{1} , {y}_{1}\right)\right)}$ is a point the line passes through.

Substituting the point from the problem gives:

$\left(y - \textcolor{red}{0}\right) = \textcolor{b l u e}{m} \left(x - \textcolor{red}{d}\right)$

$y = \textcolor{b l u e}{m} \left(x - \textcolor{red}{d}\right)$

Or translating to the more familiar slope-intercept form:

$y = \left(\textcolor{b l u e}{m} \times x\right) - \left(\textcolor{b l u e}{m} \times \textcolor{red}{d}\right)$

$y = m x - m d$