# How do you write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1.7) and perpendicular to 3x+7y= 1?

##### 1 Answer

The slope-intercept form is

#### Explanation:

**1. Find the slope for #3x+7y=1#.**

The slope of a line in

**2. Find the slope of a line perpendicular to this given line.**

Lines that are perpendicular have slopes that are negative reciprocals of each other. (One line's

**3. Plug in the known point #(x_1,y_1)# and #m# into the slope-point equation #y-y_1=m(x-x_1)#.**

Assuming the point given is

**4. Rearrange this equation into slope-intercept form.**

Solving for

**5. Rearrange (3) or (4) into standard form.**

Starting from the equation in (3), we get

(Alternatively, starting from (4), we get

which is the same equation.)

A graph of

graph{3x+7y=1 [-12.74, 9.76, -2.16, 9.095]}

For every 3 it goes down, it goes 7 right.

A graph of

graph{-7x+3y=14 [-12.74, 9.76, -2.16, 9.095]}

For every 7 it goes *up*, it goes 3 *right*.

And as you can see, this second line does indeed pass through