Question

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

Answer 1

`y = color(blue)(m)(x - color(red)(d))`

Or

`y = mx - md`

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 = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

Therefore the slope we will use to answer this question is `color(red)(m)`

The point-slope formula states: `(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))`

Where `color(blue)(m)` is the slope and `color(red)(((x_1, y_1)))` is a point the line passes through.

Substituting the point from the problem gives:

`(y - color(red)(0)) = color(blue)(m)(x - color(red)(d))`

`y = color(blue)(m)(x - color(red)(d))`

Or translating to the more familiar slope-intercept form:

`y = (color(blue)(m) xx x) - (color(blue)(m) xx color(red)(d))`

`y = mx - md`