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

Question

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

Julia Adams · Accepted Answer

#7y + x + 11 = 0#

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#.

Isaiah Anthony · Answer

undefined To find the equation of a line parallel to $x + 7y - 5 = 0$ passing through the point $ (3, -2)$, we first rewrite the given equation in slope-intercept form: $y = -\frac{1}{7}x + \frac{5}{7}$. Since parallel lines have the same slope, the slope of the desired line is also $-\frac{1}{7}$. Using the point-slope form, the equation of the line is $y + 2 = -\frac{1}{7}(x - 3)$. Simplifying gives $y = -\frac{1}{7}x + \frac{19}{7}$. Thus, the equation of the line is $y = -\frac{1}{7}x + \frac{19}{7}$.