2x - 7y +21=0; (-1, -4)

Question

It want the answer in standard form with "integer coefficients".

Answer 1

Let us assume that, the given line is paralllel to the resultant line.

The line equation is 2x - 7y + 21 = 0 and the point (- 1, - 4).

The equation 2x - 7y + 21 = 0 is adjusted in the slope - intercept form of equation or y = mx + b where m is slope and b is y - intercept.

2x - 7y + 21 = 0

7y = 2x + 21

y = ( 2/7)x + 3.

Therefore slope of given line is 2/7.

If two lines are parallel, then they have the same slope.

So, the parallel line through (- 1, - 4) has a slope of 2/7.

Now, the line equation is y = 2/7x + b.

To find the y - intercept, substitute the values of (x, y ) = (- 1, - 4) and m = 2/7 in the slope - intercept from of equation y = mx + b and solve for b.

- 4 = 2/7 * (- 1) + b

b = - 4 + (2/7) = (- 28 + 2)/7 = - 26/7.

Substitute the values of m = 2/7 and b = - 26/7 in the slope - intercept form of equation.

y = mx + b ⇒ y = (2/7)x - 26/7.

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

7y = 2x - 26

2x - 7y - 26 = 0.

The standard form of parallel line is 2x - 7y - 26 = 0.