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

1 Answer
Jarob R G.
Apr 12, 2018

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.

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