# How do you write an equation of the line given (1, 5) that are parallel to and perpendicular to the line equation y + 4x = 7?

##### 1 Answer

The line parallel to the given line is

The line perpendicular to the given line is

#### Explanation:

**Put the equation into slope-intercept form**

The slope intercept form is

This form of the equation lets you read the slope of the line directly from the equation.

Subtract

This form of the equation tells you that

the slope of the given line is

**Find the equation of the line parallel to this one, going through the point #(1,5)#**

1) All lines parallel to each other have the same slopes.

So the slope of the line parallel to the given line is also

That means that the parallel line's equation so far is

2) Now find

Sub in the values for

So the entire equation for the line parallel to the given line is

**Find the equation of the line perpendicular to the given line**

Lines that are perpendicular to each other have slopes that are the "negative inverse" of each other.

To write the slope of a line perpendicular to the given line, invert the given slope and change its sign.

In this case, that means that the slope of all the lines perpendicular to the given line have the slope

So the equation of the perpendicular line so far is

**Solve for #b#**

Sub in the values for

Clear the fraction by multiplying all the terms on both sides by

Subtract

Divide both sides by

Now you can write the entire equation for the line perpendicular to the given line and going through (1,5)