Answer:
The line A intersect line B at point (-1,-3)
Step-by-step explanation:
step 1
Find the equation of the Line A
the equation of a line in point slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=\frac{3}{2}\\point\ (3,3)](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B2%7D%5C%5Cpoint%5C%20%283%2C3%29)
substitute
![y-3=\frac{3}{2}(x-3)](https://tex.z-dn.net/?f=y-3%3D%5Cfrac%7B3%7D%7B2%7D%28x-3%29)
Convert to slope intercept form
isolate the variable y
![y-3=\frac{3}{2}x-\frac{9}{2}](https://tex.z-dn.net/?f=y-3%3D%5Cfrac%7B3%7D%7B2%7Dx-%5Cfrac%7B9%7D%7B2%7D)
![y=\frac{3}{2}x-\frac{9}{2}+3](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B2%7Dx-%5Cfrac%7B9%7D%7B2%7D%2B3)
----> equation A
step 2
Find the equation of the Line B
the equation of a line in point slope form is equal to
![y-y1=m(x-x1)](https://tex.z-dn.net/?f=y-y1%3Dm%28x-x1%29)
we have
![m=-\frac{1}{3}\\point\ (-4,-2)](https://tex.z-dn.net/?f=m%3D-%5Cfrac%7B1%7D%7B3%7D%5C%5Cpoint%5C%20%28-4%2C-2%29)
substitute
![y+2=-\frac{1}{3}(x+4)](https://tex.z-dn.net/?f=y%2B2%3D-%5Cfrac%7B1%7D%7B3%7D%28x%2B4%29)
Convert to slope intercept form
isolate the variable y
![y+2=-\frac{1}{3}x-\frac{4}{3}](https://tex.z-dn.net/?f=y%2B2%3D-%5Cfrac%7B1%7D%7B3%7Dx-%5Cfrac%7B4%7D%7B3%7D)
![y=-\frac{1}{3}x-\frac{4}{3}-2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B3%7Dx-%5Cfrac%7B4%7D%7B3%7D-2)
----> equation B
step 3
Solve the system of equations A and B by graphing
The intersection point both graphs is the solution of the system
using a graphing tool
The line A intersect line B at point (-1,-3)
see the attached figure