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:
[tex]y = \frac{3}{2} (x - 3) + 3[/tex]
Line B has a slope of -1/3 and passes through the point (-4,-2).
It's equation is
[tex]y = - \frac{1}{3} (x + 4) - 2[/tex]
To find their point of intersection, we solve the two equations simultaneously.
Let's equate the right hand sides:
[tex] \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[/tex]
Expand:
[tex]9x - 27 + 2x + 8 = - 30[/tex]
[tex]11x - 19 = - 30[/tex]
[tex]11x = - 11[/tex]
[tex]x = - 1[/tex]
Put x=-1 in the first equation:
[tex]y = \frac{3}{2} ( - 1 - 3) + 3 = - 6 + 3 = - 3[/tex]
The point of intersection is (-1,-3)
