Question

Line A has a slope of 3/2 and passes through the poin (3,3). Line B has a slope of -1/3 and passes through the point (-4,-2). At what point does line A intersect line B?

Answer 1

Answer:

The point of intersection is (-1,-3)

Step-by-step explanation:

Line A has a slope of 3/2 and passes through the point (3,3)

It is equation is:

$y = \frac{3}{2} (x - 3) + 3$

Line B has a slope of -1/3 and passes through the point (-4,-2).

It's equation is

$y = - \frac{1}{3} (x + 4) - 2$

To find their point of intersection, we solve the two equations simultaneously.

Let's equate the right hand sides:

$\frac{3}{2} (x - 3) + 3 = - \frac{1}{3} (x + 4) - 2 \\ \frac{3}{2} (x - 3) + \frac{1}{3} (x + 4) = - 5 \\ 9 (x - 3) + 2 (x + 4) = - 30$

Expand:

$9x - 27 + 2x + 8 = - 30$

$11x - 19 = - 30$

$11x = - 11$

$x = - 1$

Put x=-1 in the first equation:

$y = \frac{3}{2} ( - 1 - 3) + 3 = - 6 + 3 = - 3$

The point of intersection is (-1,-3)