How do you write the equation of the line passing through #( 3, - 2)# and parallel to : #x + 7y - 5 = 0#?

1 Answer
Apr 12, 2018

Answer:

#7y + x + 11 = 0#

Explanation:

We first find the slope of the original line, then use our slope and point to find our equation.

Slope-intercept form is a way of writing your linear equation. It is of the form #y = mx + b#, where #m# is the slope and #b# is the initial value.

If two lines are parallel, then they have the same slope. Our given equation is #x + 7y - 5 = 0#, which can be written in slope-intercept form as #y =- 1/7 x + 5/7#. The slope of both lines, then, is #-1/7#.

Now we use slope-intercept form again to find our new equation given our point #(3, -2)# and our slope #m = -1/7#. We plug in and solve for #b#,

#y = mx + b#
#y = -1/7 x + b#
#-2 = -1/7 (3) + b#
#-2 + 3/7 = b#
#b = -11/7#

Thus, our desired equation is #y = -1/7 x - 11/7#. Our original equation was in standard form, so we should put our answer in standard form.

#y = -1/7 x - 11/7#
#7y = -x - 11#
#7y + x + 11 = 0#

Our final answer is #7y + x + 11 = 0#.