write an equation of the line

Question

containing the given point and parallel to the given line. (9, -4); 3x-5y=2?

Answer 1

The line equation is 3x - 5y = 2

Write the equation in slope - intercept form y = mx + b .

Where m is slope and b is y intercept.

- 5y = - 3x + 2

y = (-3/-5)x + (2/-5)

y = (3/5)x - 2/5.

Compare the equation with slope - intercept form.

Slope (m) = 3/5

Because the parallel lines have same slopes, the slope of parallel line through the point Q(1, - 2) is 2/3.

Now the parallel line equation is y = (3/5)x + b.

Find the y - intercept by substituting the point in the parallel line equation say Q(x, y) = (9, - 4).

- 4  = (3/5)(9) + b

b = - 4 - 27/5

b = (- 20 - 27)/5

⇒ b = - 47/5.

The parallel line equation is y = (3/5)x - (47/5).