(3,-7), 6x-5y=4 equation of the line is?

Question

Find the equation of the line.

Answer 1

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

The line equation is 6x - 5y = 4 and the point (3, -7).

The equation 6x - 5y = 4 is adjusted in the slope - intercept form of equation or y = mx + b where m is slope and b is y - intercept.

6x - 5y = 4

- 5y = 4 - 6x

y = ( 6/5)x - (4/5).

Therefore slope of given line is 6/5.

So, the parallel line through (3, - 7) has a slope of 6/5.

Now, the line equation is y = 6/5x + b.

To find the y - intercept, substitute the values of (x, y ) = (3, - 7) and m = 6/5 in the slope - intercept from of equation y = mx + b and solve for b.

- 7 = 6/5 * 3 + b

b = - 7 - (18/5) = - 53/5.

Substitute the values of m = 6/5 and b = - 53/5 in the slope - intercept form of equation.

y = mx + b ⇒ y = (6/5)x - (53/5).

The equation of parallel line is y = (6/5)x - (53/5).